Research

Our research is focused on Algebraic Coding Theory: both its mathematical foundations, its computational aspects, and its applications in electronics or computer science.

 

  • [DOI] É. Barelli, P. Beelen, M. Datta, V. Neiger, and J. Rosenkilde, “Two-Point Codes for the Generalized GK Curve,” IEEE Transactions on Information Theory, vol. 64, iss. 9, p. 6268–6276, 2018.
    [Bibtex]
    @article{barelli_two-point_2018,
    title = {Two-{Point} {Codes} for the {Generalized} {GK} {Curve}},
    volume = {64},
    issn = {0018-9448},
    doi = {10.1109/TIT.2017.2763165},
    abstract = {We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti-Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes coming from the Giulietti-Korchmaros curve. Our results completely cover and in many cases improve on their results, using different techniques, while also supporting any GGK curve. Our method builds on the order bound for AG codes: to enable this, we study certain Weierstrass semigroups. This allows an efficient algorithm for computing our improved bounds. We find several new improvements upon the MinT minimum distance tables.},
    number = {9},
    journal = {IEEE Transactions on Information Theory},
    author = {Barelli, É and Beelen, P. and Datta, M. and Neiger, V. and Rosenkilde, J.},
    month = sep,
    year = {2018},
    keywords = {Linear codes, Electronic mail, Geometry, Cost accounting, codes, AG code, Europe, generalized Giulietti-Korchmaros curve, generalized GK curve, GGK curve, group theory, MinT minimum distance tables, order bound, Scholarships, two-point AG codes, two-point Weierstrass semigroup, Weierstrass semigroups},
    pages = {6268--6276},
    file = {Barelli et al. - 2018 - Two-Point Codes for the Generalized GK Curve.pdf:/home/jsrn/media/zotero/storage/4USLHEH6/Barelli et al. - 2018 - Two-Point Codes for the Generalized GK Curve.pdf:application/pdf}
    }
  • V. Neiger, J. Rosenkilde, and G. Solomatov, “Computing Popov and Hermite forms of rectangular polynomial matrices,” in International Symposium in Symbolic and Algebraic Computation, 2018.
    [Bibtex]
    @inproceedings{neiger_computing_2018,
    title = {Computing {Popov} and {Hermite} forms of rectangular polynomial matrices},
    url = {https://arxiv.org/abs/1802.01928},
    language = {en},
    urldate = {2018-10-01},
    booktitle = {International {Symposium} in {Symbolic} and {Algebraic} {Computation}},
    author = {Neiger, Vincent and Rosenkilde, Johan and Solomatov, Grigory},
    month = feb,
    year = {2018},
    file = {Neiger et al. - 2018 - Computing Popov and Hermite forms of rectangular p.pdf:/home/jsrn/media/zotero/storage/HBMB4SGV/Neiger et al. - 2018 - Computing Popov and Hermite forms of rectangular p.pdf:application/pdf}
    }
  • P. Beelen, M. Bossert, S. Puchinger, and J. Rosenkilde, “Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography,” in IEEE International Symposium on Information Theory, 2018.
    [Bibtex]
    @inproceedings{beelen_structural_2018,
    title = {Structural {Properties} of {Twisted} {Reed}-{Solomon} {Codes} with {Applications} to {Cryptography}},
    url = {https://arxiv.org/abs/1801.07003},
    language = {en},
    urldate = {2018-10-01},
    booktitle = {{IEEE} {International} {Symposium} on {Information} {Theory}},
    author = {Beelen, Peter and Bossert, Martin and Puchinger, Sven and Rosenkilde, Johan},
    month = jan,
    year = {2018},
    file = {Beelen et al. - 2018 - Structural Properties of Twisted Reed-Solomon Code.pdf:/home/jsrn/media/zotero/storage/4UWRE4G3/Beelen et al. - 2018 - Structural Properties of Twisted Reed-Solomon Code.pdf:application/pdf}
    }
  • [DOI] J. Rosenkilde, “Power Decoding of Reed–Solomon Up to the Johnson Radius,” Advances in Mathematics of Communications, vol. 12, iss. 1, p. 81–106, 2018.
    [Bibtex]
    @article{rosenkilde_power_2018,
    title = {Power {Decoding} of {Reed}–{Solomon} {Up} to the {Johnson} {Radius}},
    volume = {12},
    doi = {10.3934/amc.2018005},
    number = {1},
    journal = {Advances in Mathematics of Communications},
    author = {Rosenkilde, Johan},
    month = feb,
    year = {2018},
    pages = {81--106},
    file = {Rosenkilde - 2018 - Power Decoding of Reed–Solomon Up to the Johnson R.pdf:/home/jsrn/media/zotero/storage/NN4IGHYW/Rosenkilde - 2018 - Power Decoding of Reed–Solomon Up to the Johnson R.pdf:application/pdf}
    }
  • [DOI] S. Puchinger and J. Rosenkilde, “Decoding of interleaved Reed-Solomon codes using improved power decoding,” in IEEE International Symposium on Information Theory, 2017, p. 356–360.
    [Bibtex]
    @inproceedings{puchinger_decoding_2017,
    title = {Decoding of interleaved {Reed}-{Solomon} codes using improved power decoding},
    doi = {10.1109/ISIT.2017.8006549},
    booktitle = {{IEEE} {International} {Symposium} on {Information} {Theory}},
    author = {Puchinger, S. and Rosenkilde, Johan},
    month = jun,
    year = {2017},
    keywords = {Approximation algorithms, collaborative decoding, Complexity theory, computational complexity, Decoding, improved power decoding, Indexes, Interleaved codes, interleaved Reed-Solomon codes, IRS codes, Johnson radius, m-interleaved Reed-Solomon codes, Mathematical model, Measurement, partial decoding algorithm, Power Decoding with Multiplicities, probability, random error, Reed-Solomon codes, time polynomial},
    pages = {356--360},
    file = {Puchinger and Nielsen - 2017 - Decoding of interleaved Reed-Solomon codes using i.pdf:/home/jsrn/media/zotero/storage/GX4K8ES6/Puchinger and Nielsen - 2017 - Decoding of interleaved Reed-Solomon codes using i.pdf:application/pdf}
    }
  • [DOI] P. Beelen, S. Puchinger, and J. Rosenkilde, “Twisted Reed-Solomon Codes,” in IEEE International Symposium on Information Theory (ISIT), 2017, p. 336–340.
    [Bibtex]
    @inproceedings{beelen_twisted_2017,
    title = {Twisted {Reed}-{Solomon} {Codes}},
    doi = {10.1109/ISIT.2017.8006545},
    abstract = {We present a new general construction of MDS codes over a finite field Fq. We describe two explicit subclasses which contain new MDS codes of length at least q/2 for all values of q ≥ 11. Moreover, we show that most of the new codes are not equivalent to a Reed-Solomon code.},
    booktitle = {{IEEE} {International} {Symposium} on {Information} {Theory} ({ISIT})},
    author = {Beelen, P. and Puchinger, S. and Rosenkilde, Johan},
    month = jun,
    year = {2017},
    keywords = {Computer science, Finite field, general construction, Generators, Indexes, Linear codes, Mathematics, maximum distance separable codes, MDS codes, Measurement, Reed-Solomon codes, twisted Reed-Solomon codes},
    pages = {336--340},
    file = {Beelen et al. - 2017 - Twisted reed-solomon codes.pdf:/home/jsrn/media/zotero/storage/RH2524I4/Beelen et al. - 2017 - Twisted reed-solomon codes.pdf:application/pdf}
    }
  • [DOI] S. Puchinger, J. Rosenkilde, W. Li, and V. Sidorenko, “Row reduction applied to decoding of rank-metric and subspace codes,” Designs, Codes and Cryptography, vol. 82, iss. 1-2, p. 389–409, 2017.
    [Bibtex]
    @article{puchinger_row_2017,
    title = {Row reduction applied to decoding of rank-metric and subspace codes},
    volume = {82},
    issn = {0925-1022, 1573-7586},
    url = {https://link.springer.com/article/10.1007/s10623-016-0257-9},
    doi = {10.1007/s10623-016-0257-9},
    abstract = {We show that decoding of ℓ{\textbackslash}ell -Interleaved Gabidulin codes, as well as list-ℓ{\textbackslash}ell decoding of Mahdavifar–Vardy (MV) codes can be performed by row reducing skew polynomial matrices. Inspired by row reduction of F[x]{\textbackslash}mathbb \{F\}[x] matrices, we develop a general and flexible approach of transforming matrices over skew polynomial rings into a certain reduced form. We apply this to solve generalised shift register problems over skew polynomial rings which occur in decoding ℓ{\textbackslash}ell -Interleaved Gabidulin codes. We obtain an algorithm with complexity O(ℓμ2)O({\textbackslash}ell {\textbackslash}mu {\textasciicircum}2) where μ{\textbackslash}mu measures the size of the input problem and is proportional to the code length n in the case of decoding. Further, we show how to perform the interpolation step of list-ℓ{\textbackslash}ell -decoding MV codes in complexity O(ℓn2)O({\textbackslash}ell n{\textasciicircum}2), where n is the number of interpolation constraints.},
    language = {en},
    number = {1-2},
    urldate = {2017-03-01},
    journal = {Designs, Codes and Cryptography},
    author = {Puchinger, Sven and Rosenkilde, Johan and Li, Wenhui and Sidorenko, Vladimir},
    month = jan,
    year = {2017},
    pages = {389--409},
    file = {Puchinger et al. - 2017 - Row reduction applied to decoding of rank-metric a.pdf:/home/jsrn/media/zotero/storage/EEH6VAEX/Puchinger et al. - 2017 - Row reduction applied to decoding of rank-metric a.pdf:application/pdf}
    }
  • [DOI] V. Neiger, J. Rosenkilde, and É. Schost, “Fast Computation of the Roots of Polynomials Over the Ring of Power Series,” in International Symposium on Symbolic and Algebraic Computation, 2017.
    [Bibtex]
    @inproceedings{neiger_fast_2017,
    title = {Fast {Computation} of the {Roots} of {Polynomials} {Over} the {Ring} of {Power} {Series}},
    url = {https://hal.inria.fr/hal-01457954/document},
    doi = {10.1145/3087604.3087642},
    language = {en},
    urldate = {2017-09-21},
    booktitle = {International {Symposium} on {Symbolic} and {Algebraic} {Computation}},
    author = {Neiger, Vincent and Rosenkilde, Johan and Schost, Éric},
    month = jul,
    year = {2017},
    file = {Neiger et al. - 2017 - Fast Computation of the Roots of Polynomials Over .pdf:/home/jsrn/media/zotero/storage/GU2HHQI6/Neiger et al. - 2017 - Fast Computation of the Roots of Polynomials Over .pdf:application/pdf}
    }
  • [DOI] M. Khochtali, J. Rosenkilde, and A. Storjohann, “Popov form computation for matrices of Ore polynomials,” in International Symposium on Symbolic and Algebraic Computation, 2017, p. 253–260.
    [Bibtex]
    @inproceedings{khochtali_popov_2017,
    title = {Popov form computation for matrices of {Ore} polynomials},
    isbn = {978-1-4503-5064-8},
    url = {http://www.forskningsdatabasen.dk/en/catalog/2373300044},
    doi = {10.1145/3087604.3087650},
    language = {eng},
    urldate = {2018-02-07},
    booktitle = {International {Symposium} on {Symbolic} and {Algebraic} {Computation}},
    publisher = {The Association for Computing Machinery},
    author = {Khochtali, Mohamed and Rosenkilde, Johan and Storjohann, Arne},
    year = {2017},
    pages = {253--260},
    file = {Khochtali et al. - 2017 - Popov form computation for matrices of Ore polynom.pdf:/home/jsrn/media/zotero/storage/7L5AUKZF/Khochtali et al. - 2017 - Popov form computation for matrices of Ore polynom.pdf:application/pdf}
    }
  • S. Puchinger, J. Rosenkilde, and I. Bouw, “Improved Power Decoding of One-Point Hermitian Codes,” in International Workshop in Coding Theory and Cryptography, 2017.
    [Bibtex]
    @inproceedings{puchinger_improved_2017,
    title = {Improved {Power} {Decoding} of {One}-{Point} {Hermitian} {Codes}},
    url = {https://arxiv.org/abs/1703.07982},
    urldate = {2017-11-23},
    booktitle = {International {Workshop} in {Coding} {Theory} and {Cryptography}},
    author = {Puchinger, Sven and Rosenkilde, Johan and Bouw, Irene},
    year = {2017},
    file = {Puchinger et al. - 2017 - Improved Power Decoding of One-Point Hermitian Cod.pdf:/home/jsrn/media/zotero/storage/KA3KHU5P/Puchinger et al. - 2017 - Improved Power Decoding of One-Point Hermitian Cod.pdf:application/pdf}
    }
  • S. Puchinger, J. Rosenkilde, and J. Sheekey, “Further Generalisations of Twisted Gabidulin Codes,” in International Workshop in Coding Theory and Cryptography, 2017.
    [Bibtex]
    @inproceedings{puchinger_further_2017,
    title = {Further {Generalisations} of {Twisted} {Gabidulin} {Codes}},
    url = {https://arxiv.org/abs/1703.08093},
    urldate = {2017-11-23},
    booktitle = {International {Workshop} in {Coding} {Theory} and {Cryptography}},
    author = {Puchinger, Sven and Rosenkilde, Johan and Sheekey, John},
    year = {2017},
    file = {Puchinger et al. - 2017 - Further Generalisations of Twisted Gabidulin Codes.pdf:/home/jsrn/media/zotero/storage/NHEW8UIU/Puchinger et al. - 2017 - Further Generalisations of Twisted Gabidulin Codes.pdf:application/pdf}
    }
  • S. Puchinger, S. Müelich, D. Mödinger, J. Rosenkilde, and M. Bossert, “Decoding Interleaved Gabidulin Codes using Alekhnovich’s Algorithm,” in International Workshop in Algebraic and Combinatorial Coding Theory, 2016.
    [Bibtex]
    @inproceedings{puchinger_decoding_2016,
    title = {Decoding {Interleaved} {Gabidulin} {Codes} using {Alekhnovich}'s {Algorithm}},
    url = {http://arxiv.org/abs/1604.05899},
    urldate = {2016-10-04},
    booktitle = {International {Workshop} in {Algebraic} and {Combinatorial} {Coding} {Theory}},
    author = {Puchinger, Sven and Müelich, Sven and Mödinger, David and Rosenkilde, Johan and Bossert, Martin},
    year = {2016},
    note = {arXiv: 1604.05899},
    keywords = {Computer Science - Information Theory, Computer Science - Symbolic Computation},
    file = {Puchinger et al. - 2016 - Decoding Interleaved Gabidulin Codes using Alekhno.pdf:/home/jsrn/media/zotero/storage/TCVXEK54/Puchinger et al. - 2016 - Decoding Interleaved Gabidulin Codes using Alekhno.pdf:application/pdf}
    }
  • [DOI] J. Rosenkilde and A. Storjohann, “Algorithms for Simultaneous Padé Approximations,” in Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, New York, NY, USA, 2016, p. 405–412.
    [Bibtex]
    @inproceedings{rosenkilde_algorithms_2016,
    address = {New York, NY, USA},
    series = {{ISSAC} '16},
    title = {Algorithms for {Simultaneous} {Padé} {Approximations}},
    isbn = {978-1-4503-4380-0},
    url = {http://doi.acm.org/10.1145/2930889.2930933},
    doi = {10.1145/2930889.2930933},
    abstract = {We describe how to solve simultaneous Padé approximations over a power series ring K[[x]] for a field K using O{\textasciitilde}(nω - 1 d) operations in K, where d is the sought precision and \$n\$ is the number of power series to approximate. We develop two algorithms using different approaches. Both algorithms return a reduced sub-bases that generates the complete set of solutions to the input approximations problem that satisfy the given degree constraints. Our results are made possible by recent breakthroughs in fast computations of minimal approximant bases and Hermite Padé approximations.},
    urldate = {2016-09-20},
    booktitle = {Proceedings of the {ACM} on {International} {Symposium} on {Symbolic} and {Algebraic} {Computation}},
    publisher = {ACM},
    author = {Rosenkilde, Johan and Storjohann, Arne},
    year = {2016},
    keywords = {polynomials, Pad' approximation, approximations},
    pages = {405--412},
    file = {Rosenkilde né Nielsen and Storjohann - 2016 - Algorithms for Simultaneous Padé Approximations.pdf:/home/jsrn/media/zotero/storage/3HRE4M5W/Rosenkilde né Nielsen and Storjohann - 2016 - Algorithms for Simultaneous Padé Approximations.pdf:application/pdf}
    }
  • [DOI] J. S. R. Nielsen and P. Beelen, “Sub-Quadratic Decoding of One-Point Hermitian Codes,” IEEE Transactions on Information Theory, vol. 61, iss. 6, p. 3225–3240, 2015.
    [Bibtex]
    @article{nielsen_sub-quadratic_2015,
    title = {Sub-{Quadratic} {Decoding} of {One}-{Point} {Hermitian} {Codes}},
    volume = {61},
    issn = {0018-9448},
    doi = {10.1109/TIT.2015.2424415},
    abstract = {We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realization of the Guruswami-Sudan algorithm using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimization. The second is a power decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the matrix minimization algorithms from computer algebra, yielding similar asymptotic complexities.},
    number = {6},
    journal = {IEEE Transactions on Information Theory},
    author = {Nielsen, J.S.R. and Beelen, P.},
    month = jun,
    year = {2015},
    keywords = {interpolation, polynomials, Complexity theory, Decoding, Indexes, list decoding, power decoding, Guruswami-Sudan algorithm, Guruswami–Sudan, computer algebra, minimisation, matrix algebra, Sudan radius, key equation decoding, matrix minimization algorithms, one-point hHermitian codes, polynomial ring matrix minimization, power decoding algorithm, probabilistic decoding algorithm, similar asymptotic complexities, subquadratic complexity decoding algorithms, subquadratic decoding, Minimization, Standards, AG codes, Guruswami???Sudan, Hermitian codes},
    pages = {3225--3240},
    file = {Nielsen and Beelen - 2015 - Sub-Quadratic Decoding of One-Point Hermitian Code.pdf:/home/jsrn/media/zotero/storage/KRS2S6VN/Nielsen and Beelen - 2015 - Sub-Quadratic Decoding of One-Point Hermitian Code.pdf:application/pdf}
    }
  • [DOI] J. S. R. Nielsen and P. Beelen, “Sub-quadratic decoding of one-point Hermitian codes,” IEEE Trans. Inform. Theory, vol. 61, iss. 6, p. 3225–3240, 2015.
    [Bibtex]
    @article {MR3352496,
    AUTHOR = {Nielsen, Johan S. R. and Beelen, Peter},
    TITLE = {Sub-quadratic decoding of one-point {H}ermitian codes},
    JOURNAL = {IEEE Trans. Inform. Theory},
    FJOURNAL = {Institute of Electrical and Electronics Engineers.
    Transactions on Information Theory},
    VOLUME = {61},
    YEAR = {2015},
    NUMBER = {6},
    PAGES = {3225--3240},
    ISSN = {0018-9448},
    MRCLASS = {94B60 (94B35)},
    DOI = {10.1109/TIT.2015.2424415},
    URL = {http://dx.doi.org/10.1109/TIT.2015.2424415},
    }
  • [DOI] M. A. Abdelraheem, P. Beelen, A. Bogdanov, and E. Tischhauser, “Twisted polynomials and forgery attacks on GCM,” in Advances in cryptology–-EUROCRYPT 2015. Part I, Springer, Heidelberg, 2015, vol. 9056, p. 762–786.
    [Bibtex]
    @incollection {MR3344945,
    AUTHOR = {Abdelraheem, Mohamed Ahmed and Beelen, Peter and Bogdanov,
    Andrey and Tischhauser, Elmar},
    TITLE = {Twisted polynomials and forgery attacks on {GCM}},
    BOOKTITLE = {Advances in cryptology---{EUROCRYPT} 2015. {P}art {I}},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {9056},
    PAGES = {762--786},
    PUBLISHER = {Springer, Heidelberg},
    YEAR = {2015},
    MRCLASS = {94A60},
    DOI = {10.1007/978-3-662-46800-5_29},
    URL = {http://dx.doi.org/10.1007/978-3-662-46800-5_29},
    }
  • A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth, “Towers of function fields over non-prime finite fields,” Mosc. Math. J., vol. 15, iss. 1, p. 1–29, 181, 2015.
    [Bibtex]
    @article {MR3427409,
    AUTHOR = {Bassa, Alp and Beelen, Peter and Garcia, Arnaldo and
    Stichtenoth, Henning},
    TITLE = {Towers of function fields over non-prime finite fields},
    JOURNAL = {Mosc. Math. J.},
    FJOURNAL = {Moscow Mathematical Journal},
    VOLUME = {15},
    YEAR = {2015},
    NUMBER = {1},
    PAGES = {1--29, 181},
    ISSN = {1609-3321},
    MRCLASS = {11R58 (11G09 11G20)},
    }
  • [DOI] P. Beelen, S. R. Ghorpade, and S. U. Hasan, “Linear codes associated to determinantal varieties,” Discrete Math., vol. 338, iss. 8, p. 1493–1500, 2015.
    [Bibtex]
    @article {MR3336120,
    AUTHOR = {Beelen, Peter and Ghorpade, Sudhir R. and Hasan, Sartaj Ul},
    TITLE = {Linear codes associated to determinantal varieties},
    JOURNAL = {Discrete Math.},
    FJOURNAL = {Discrete Mathematics},
    VOLUME = {338},
    YEAR = {2015},
    NUMBER = {8},
    PAGES = {1493--1500},
    ISSN = {0012-365X},
    MRCLASS = {94B05},
    DOI = {10.1016/j.disc.2015.03.009},
    URL = {http://dx.doi.org/10.1016/j.disc.2015.03.009},
    }
  • W. Li, J. S. R. Nielsen, S. Puchinger, and V. Sidorenko, “Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation,” in International Workshop on Coding and Cryptography, 2015.
    [Bibtex]
    @inproceedings{li_solving_2015,
    title = {Solving {Shift} {Register} {Problems} over {Skew} {Polynomial} {Rings} using {Module} {Minimisation}},
    url = {http://arxiv.org/abs/1501.04797},
    abstract = {For many algebraic codes the main part of decoding can be reduced to a shift register synthesis problem. In this paper we present an approach for solving generalised shift register problems over skew polynomial rings which occur in error and erasure decoding of \${\textbackslash}ell\$-Interleaved Gabidulin codes. The algorithm is based on module minimisation and has time complexity \$O({\textbackslash}ell {\textbackslash}mu{\textasciicircum}2)\$ where \${\textbackslash}mu\$ measures the size of the input problem.},
    urldate = {2015-09-18},
    booktitle = {International {Workshop} on {Coding} and {Cryptography}},
    author = {Li, Wenhui and Nielsen, Johan S. R. and Puchinger, Sven and Sidorenko, Vladimir},
    month = apr,
    year = {2015},
    note = {arXiv: 1501.04797},
    keywords = {Computer Science - Information Theory},
    file = {Li et al. - 2015 - Solving Shift Register Problems over Skew Polynomi.pdf:/home/jsrn/media/zotero/storage/PU7VI284/Li et al. - 2015 - Solving Shift Register Problems over Skew Polynomi.pdf:application/pdf}
    }
  • [DOI] A. Bassa, P. Beelen, and N. Nguyen, “Good families of Drinfeld modular curves,” LMS J. Comput. Math., vol. 18, iss. 1, p. 699–712, 2015.
    [Bibtex]
    @article {MR3433893,
    AUTHOR = {Bassa, Alp and Beelen, Peter and Nguyen, Nhut},
    TITLE = {Good families of {D}rinfeld modular curves},
    JOURNAL = {LMS J. Comput. Math.},
    FJOURNAL = {LMS Journal of Computation and Mathematics},
    VOLUME = {18},
    YEAR = {2015},
    NUMBER = {1},
    PAGES = {699--712},
    ISSN = {1461-1570},
    MRCLASS = {11G09 (11R58 14H05 14H10 14Q05)},
    DOI = {10.1112/S146115701500025X},
    URL = {http://dx.doi.org/10.1112/S146115701500025X},
    }
  • J. S. R. Nielsen, “Power Decoding of Reed–Solomon Up to the Johnson Radius,” in International Workshop on Algebraic and Combinatorial Coding Theory, 2014.
    [Bibtex]
    @inproceedings{nielsen_power_2014-1,
    title = {Power {Decoding} of {Reed}–{Solomon} {Up} to the {Johnson} {Radius}},
    url = {http://jsrn.dk/publications.html#2014-acct-powermults},
    booktitle = {International {Workshop} on {Algebraic} and {Combinatorial} {Coding} {Theory}},
    author = {Nielsen, Johan S. R.},
    month = sep,
    year = {2014}
    }
  • A. Bassa, P. Beelen, and N. Nguyen, “Good towers of function fields,” in Algebraic curves and finite fields, De Gruyter, Berlin, 2014, vol. 16, p. 23–40.
    [Bibtex]
    @incollection {MR3287681,
    AUTHOR = {Bassa, Alp and Beelen, Peter and Nguyen, Nhut},
    TITLE = {Good towers of function fields},
    BOOKTITLE = {Algebraic curves and finite fields},
    SERIES = {Radon Ser. Comput. Appl. Math.},
    VOLUME = {16},
    PAGES = {23--40},
    PUBLISHER = {De Gruyter, Berlin},
    YEAR = {2014},
    MRCLASS = {14H05 (11R58 14G15)},
    }
  • M. H. Mohamed, J. S. R. Nielsen, and M. Bossert, “Reduced List Decoding of Reed–Solomon Codes Using Reliability Information,” in International Symposium on Mathematical Theory of Networks and Systems, 2014.
    [Bibtex]
    @inproceedings{mohamed_reduced_2014,
    title = {Reduced {List} {Decoding} of {Reed}–{Solomon} {Codes} {Using} {Reliability} {Information}},
    url = {http://jsrn.dk/publications.html#2014-mtns-reducedwu},
    urldate = {2014-03-27},
    booktitle = {International {Symposium} on {Mathematical} {Theory} of {Networks} and {Systems}},
    author = {Mohamed, Mostafa H. and Nielsen, Johan S. R. and Bossert, Martin},
    year = {2014},
    file = {Mohamed et al. - 2014 - Reduced List Decoding of Reed–Solomon Codes Using .pdf:/home/jsrn/media/zotero/storage/6SXVQFSC/Mohamed et al. - 2014 - Reduced List Decoding of Reed–Solomon Codes Using .pdf:application/pdf}
    }
  • J. S. R. Nielsen, “Solving generalised Padé approximations over polynomial rings,” in Preprint, 2014.
    [Bibtex]
    @inproceedings{nielsen_solving_2014,
    title = {Solving generalised {Padé} approximations over polynomial rings},
    url = {http://jsrn.dk/publications.html#2014-pade},
    urldate = {2014-02-28},
    booktitle = {Preprint},
    author = {Nielsen, Johan S. R.},
    month = jan,
    year = {2014},
    note = {Available at http://jsrn.dk/},
    file = {Nielsen - 2014 - Solving generalised Padé approximations over polyn.pdf:/home/jsrn/media/zotero/storage/IZ79SDZ8/Nielsen - 2014 - Solving generalised Padé approximations over polyn.pdf:application/pdf}
    }
  • J. S. R. Nielsen, “Power Decoding of Reed–Solomon Codes Revisited,” in International Castle Meeting on Coding Theory and Applications, 2014.
    [Bibtex]
    @inproceedings{nielsen_power_2014,
    title = {Power {Decoding} of {Reed}–{Solomon} {Codes} {Revisited}},
    url = {http://jsrn.dk/publications.html#2014-icmcta-powergao},
    booktitle = {International {Castle} {Meeting} on {Coding} {Theory} and {Applications}},
    author = {Nielsen, Johan S. R.},
    month = sep,
    year = {2014},
    file = {Nielsen - 2014 - Power Decoding of Reed–Solomon Codes Revisited.pdf:/home/jsrn/media/zotero/storage/WPBPX98U/Nielsen - 2014 - Power Decoding of Reed–Solomon Codes Revisited.pdf:application/pdf}
    }
  • [DOI] A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth, “Galois towers over non-prime finite fields,” Acta Arith., vol. 164, iss. 2, p. 163–179, 2014.
    [Bibtex]
    @article {MR3224833,
    AUTHOR = {Bassa, Alp and Beelen, Peter and Garcia, Arnaldo and
    Stichtenoth, Henning},
    TITLE = {Galois towers over non-prime finite fields},
    JOURNAL = {Acta Arith.},
    FJOURNAL = {Acta Arithmetica},
    VOLUME = {164},
    YEAR = {2014},
    NUMBER = {2},
    PAGES = {163--179},
    ISSN = {0065-1036},
    MRCLASS = {11R32 (11G20 11R58)},
    DOI = {10.4064/aa164-2-6},
    URL = {http://dx.doi.org/10.4064/aa164-2-6},
    }
  • [DOI] A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth, “An improvement of the Gilbert-Varshamov bound over nonprime fields,” IEEE Trans. Inform. Theory, vol. 60, iss. 7, p. 3859–3861, 2014.
    [Bibtex]
    @article {MR3225935,
    AUTHOR = {Bassa, Alp and Beelen, Peter and Garcia, Arnaldo and
    Stichtenoth, Henning},
    TITLE = {An improvement of the {G}ilbert-{V}arshamov bound over
    nonprime fields},
    JOURNAL = {IEEE Trans. Inform. Theory},
    FJOURNAL = {Institute of Electrical and Electronics Engineers.
    Transactions on Information Theory},
    VOLUME = {60},
    YEAR = {2014},
    NUMBER = {7},
    PAGES = {3859--3861},
    ISSN = {0018-9448},
    MRCLASS = {94B25},
    DOI = {10.1109/TIT.2014.2316531},
    URL = {http://dx.doi.org/10.1109/TIT.2014.2316531},
    }
  • J. S. R. Nielsen, “Fast Kötter-Nielsen-Høholdt Interpolation in the Guruswami-Sudan Algorithm.” 2014.
    [Bibtex]
    @inproceedings{nielsen_fast_2014,
    title = {Fast {Kötter}-{Nielsen}-{Høholdt} {Interpolation} in the {Guruswami}-{Sudan} {Algorithm}},
    url = {http://jsrn.dk/publications.html#2014-fast_knh},
    author = {Nielsen, J.S.R.},
    year = {2014},
    file = {Nielsen - 2014 - Fast Kötter-Nielsen-Høholdt Interpolation in the G.pdf:/home/jsrn/media/zotero/storage/USXA89S6/Nielsen - 2014 - Fast Kötter-Nielsen-Høholdt Interpolation in the G.pdf:application/pdf}
    }
  • [DOI] J. S. R. Nielsen and A. Zeh, “Multi-Trial Guruswami–Sudan Decoding for Generalised Reed–Solomon Codes,” Designs, Codes and Cryptography, iss. Special issue on Coding and Cryptography, 2014.
    [Bibtex]
    @article{nielsen_multi-trial_2014,
    title = {Multi-{Trial} {Guruswami}–{Sudan} {Decoding} for {Generalised} {Reed}–{Solomon} {Codes}},
    issn = {0925-1022, 1573-7586},
    url = {http://link.springer.com/article/10.1007/s10623-014-9951-7},
    doi = {10.1007/s10623-014-9951-7},
    abstract = {An iterated refinement procedure for the Guruswami–Sudan list decoding algorithm for Generalised Reed–Solomon codes based on Alekhnovich’s module minimisation is proposed. The method is parametrisable and allows variants of the usual list decoding approach. In particular, finding the list of closest codewords within an intermediate radius can be performed with improved average-case complexity while retaining the worst-case complexity. We provide a detailed description of the module minimisation, reanalysing the Mulders–Storjohann algorithm and drawing new connections to both Alekhnovich’s algorithm and Lee–O’Sullivan’s. Furthermore, we show how to incorporate the re-encoding technique of Kötter and Vardy into our iterative algorithm.},
    language = {en},
    number = {Special issue on Coding and Cryptography},
    urldate = {2014-04-18},
    journal = {Designs, Codes and Cryptography},
    author = {Nielsen, Johan S. R. and Zeh, Alexander},
    month = mar,
    year = {2014},
    keywords = {Reed–Solomon codes, list decoding, Coding and Information Theory, Combinatorics, Data Encryption, Discrete Mathematics in Computer Science, Data Structures, Cryptology and Information Theory, Information and Communication, Circuits, 94B35, Guruswami–Sudan, Multi-trial, Re-encoding transformation, 68P30},
    file = {Nielsen and Zeh - 2014 - Multi-Trial Guruswami–Sudan Decoding for Generalis.pdf:/home/jsrn/media/zotero/storage/D3SS4DBG/Nielsen and Zeh - 2014 - Multi-Trial Guruswami–Sudan Decoding for Generalis.pdf:application/pdf}
    }
  • J. S. R. Nielsen, “List Decoding of Algebraic Codes,” {PhD} {Thesis} PhD Thesis, 2013.
    [Bibtex]
    @phdthesis{nielsen_list_2013,
    type = {{PhD} {Thesis}},
    title = {List {Decoding} of {Algebraic} {Codes}},
    url = {http://jsrn.dk/publications.html#2013-phd},
    school = {Technical University of Denmark},
    author = {Nielsen, Johan S. R.},
    year = {2013},
    file = {Nielsen - 2013 - List Decoding of Algebraic Codes.pdf:/home/jsrn/media/zotero/storage/UW4I2VIN/Nielsen - 2013 - List Decoding of Algebraic Codes.pdf:application/pdf}
    }
  • [DOI] P. Beelen, T. Høholdt, J. S. R. Nielsen, and Y. Wu, “On Rational Interpolation-Based List-Decoding and List-Decoding Binary Goppa Codes,” IEEE Transactions on Information Theory, vol. 59, iss. 6, p. 3269–3281, 2013.
    [Bibtex]
    @article{beelen_rational_2013,
    title = {On {Rational} {Interpolation}-{Based} {List}-{Decoding} and {List}-{Decoding} {Binary} {Goppa} {Codes}},
    volume = {59},
    issn = {0018-9448, 1557-9654},
    url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6459024},
    doi = {10.1109/TIT.2013.2243800},
    number = {6},
    urldate = {2013-05-20},
    journal = {IEEE Transactions on Information Theory},
    author = {Beelen, Peter and Høholdt, Tom and Nielsen, Johan S. R. and Wu, Yingquan},
    month = jun,
    year = {2013},
    pages = {3269--3281},
    file = {Beelen et al. - 2013 - On Rational Interpolation-Based List-Decoding and .pdf:/home/jsrn/media/zotero/storage/J65K25M5/Beelen et al. - 2013 - On Rational Interpolation-Based List-Decoding and .pdf:application/pdf}
    }
  • J. S. R. Nielsen and A. Zeh, “Multi-Trial Guruswami–Sudan Decoding for Generalised Reed–Solomon Codes,” in International Workshop on Coding and Cryptography, 2013.
    [Bibtex]
    @inproceedings{nielsen_multi-trial_2013,
    title = {Multi-{Trial} {Guruswami}--{Sudan} {Decoding} for {Generalised} {Reed}--{Solomon} {Codes}},
    url = {http://jsrn.dk/publications.html#2013-wcc-multi-trial},
    booktitle = {International {Workshop} on {Coding} and {Cryptography}},
    author = {Nielsen, Johan S. R. and Zeh, Alexander},
    year = {2013},
    file = {Nielsen and Zeh - 2013 - Multi-Trial Guruswami--Sudan Decoding for Generali.pdf:/home/jsrn/media/zotero/storage/M4B3A8SP/Nielsen and Zeh - 2013 - Multi-Trial Guruswami--Sudan Decoding for Generali.pdf:application/pdf}
    }
  • [DOI] W. Li, V. Sidorenko, and J. S. R. Nielsen, “On Decoding Interleaved Chinese Remainder Codes,” in IEEE International Symposium on Information Theory, 2013.
    [Bibtex]
    @inproceedings{li_decoding_2013,
    title = {On {Decoding} {Interleaved} {Chinese} {Remainder} {Codes}},
    url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6620387},
    doi = {10.1109/ISIT.2013.6620387},
    booktitle = {{IEEE} {International} {Symposium} on {Information} {Theory}},
    author = {Li, W. and Sidorenko, V. and Nielsen, Johan S. R.},
    year = {2013},
    file = {Li et al. - 2013 - On Decoding Interleaved Chinese Remainder Codes.pdf:/home/jsrn/media/zotero/storage/6XDDR5TI/Li et al. - 2013 - On Decoding Interleaved Chinese Remainder Codes.pdf:application/pdf}
    }
  • [DOI] P. Beelen and D. Ruano, “Bounding the number of points on a curve using a generalization of Weierstrass semigroups,” Des. Codes Cryptogr., vol. 66, iss. 1-3, p. 221–230, 2013.
    [Bibtex]
    @article {MR3016565,
    AUTHOR = {Beelen, Peter and Ruano, Diego},
    TITLE = {Bounding the number of points on a curve using a
    generalization of {W}eierstrass semigroups},
    JOURNAL = {Des. Codes Cryptogr.},
    FJOURNAL = {Designs, Codes and Cryptography. An International Journal},
    VOLUME = {66},
    YEAR = {2013},
    NUMBER = {1-3},
    PAGES = {221--230},
    ISSN = {0925-1022},
    MRCLASS = {14G15 (11G20 14G50 14H05)},
    DOI = {10.1007/s10623-012-9685-3},
    URL = {http://dx.doi.org/10.1007/s10623-012-9685-3},
    }
  • [DOI] P. Beelen, T. H{o}holdt, J. S. R. Nielsen, and Y. Wu, “On rational interpolation-based list-decoding and list-decoding binary Goppa codes,” IEEE Trans. Inform. Theory, vol. 59, iss. 6, p. 3269–3281, 2013.
    [Bibtex]
    @article {MR3061245,
    AUTHOR = {Beelen, Peter and H{\o}holdt, Tom and Nielsen, Johan S. R. and
    Wu, Yingquan},
    TITLE = {On rational interpolation-based list-decoding and
    list-decoding binary {G}oppa codes},
    JOURNAL = {IEEE Trans. Inform. Theory},
    FJOURNAL = {Institute of Electrical and Electronics Engineers.
    Transactions on Information Theory},
    VOLUME = {59},
    YEAR = {2013},
    NUMBER = {6},
    PAGES = {3269--3281},
    ISSN = {0018-9448},
    MRCLASS = {94B05},
    DOI = {10.1109/TIT.2013.2243800},
    URL = {http://dx.doi.org/10.1109/TIT.2013.2243800},
    }
  • P. Beelen, “Affine Grassmann codes: an overview,” in From modern coding theory to postmodern coding theory (Japanese), Kyushu Univ. Fac. Math., Fukuoka, 2013, vol. 44, p. 77–85.
    [Bibtex]
    @incollection {MR3074823,
    AUTHOR = {Beelen, Peter},
    TITLE = {Affine {G}rassmann codes: an overview},
    BOOKTITLE = {From modern coding theory to postmodern coding theory
    ({J}apanese)},
    SERIES = {COE Lect. Note},
    VOLUME = {44},
    PAGES = {77--85},
    PUBLISHER = {Kyushu Univ. Fac. Math., Fukuoka},
    YEAR = {2013},
    MRCLASS = {94B40},
    }
  • [DOI] J. S. R. Nielsen, “Generalised Multi-sequence Shift-Register Synthesis using Module Minimisation,” in IEEE International Symposium on Information Theory, 2013, p. 882–886.
    [Bibtex]
    @inproceedings{nielsen_generalised_2013,
    title = {Generalised {Multi}-sequence {Shift}-{Register} {Synthesis} using {Module} {Minimisation}},
    url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6620353},
    doi = {10.1109/ISIT.2013.6620353},
    booktitle = {{IEEE} {International} {Symposium} on {Information} {Theory}},
    author = {Nielsen, Johan S. R.},
    year = {2013},
    pages = {882--886},
    file = {Nielsen - 2013 - Generalised Multi-sequence Shift-Register Synthesi.pdf:/home/jsrn/media/zotero/storage/RJ2GJKD7/Nielsen - 2013 - Generalised Multi-sequence Shift-Register Synthesi.pdf:application/pdf}
    }
  • [DOI] P. Beelen and G. Leander, “A new construction of highly nonlinear S-boxes,” Cryptogr. Commun., vol. 4, iss. 1, p. 65–77, 2012.
    [Bibtex]
    @article {MR2886646,
    AUTHOR = {Beelen, Peter and Leander, Gregor},
    TITLE = {A new construction of highly nonlinear {S}-boxes},
    JOURNAL = {Cryptogr. Commun.},
    FJOURNAL = {Cryptography and Communications},
    VOLUME = {4},
    YEAR = {2012},
    NUMBER = {1},
    PAGES = {65--77},
    ISSN = {1936-2447},
    MRCLASS = {06E30 (65T50 94B05 94C10)},
    DOI = {10.1007/s12095-011-0052-4},
    URL = {http://dx.doi.org/10.1007/s12095-011-0052-4},
    }
  • [DOI] H. Aref, P. Beelen, and M. Br{o}ns, “Bilinear relative equilibria of identical point vortices,” J. Nonlinear Sci., vol. 22, iss. 5, p. 849–885, 2012.
    [Bibtex]
    @article {MR2982054,
    AUTHOR = {Aref, H. and Beelen, P. and Br{\o}ns, M.},
    TITLE = {Bilinear relative equilibria of identical point vortices},
    JOURNAL = {J. Nonlinear Sci.},
    FJOURNAL = {Journal of Nonlinear Science},
    VOLUME = {22},
    YEAR = {2012},
    NUMBER = {5},
    PAGES = {849--885},
    ISSN = {0938-8974},
    MRCLASS = {76B47 (34A05 34M03)},
    DOI = {10.1007/s00332-012-9129-2},
    URL = {http://dx.doi.org/10.1007/s00332-012-9129-2},
    }
  • [DOI] A. Bassa and P. Beelen, “A closed-form expression for the Drinfeld modular polynomial $\Phi_T(X,Y)$,” Arch. Math. (Basel), vol. 99, iss. 3, p. 237–245, 2012.
    [Bibtex]
    @article {MR2969029,
    AUTHOR = {Bassa, Alp and Beelen, Peter},
    TITLE = {A closed-form expression for the {D}rinfeld modular polynomial
    {$\Phi_T(X,Y)$}},
    JOURNAL = {Arch. Math. (Basel)},
    FJOURNAL = {Archiv der Mathematik},
    VOLUME = {99},
    YEAR = {2012},
    NUMBER = {3},
    PAGES = {237--245},
    ISSN = {0003-889X},
    CODEN = {ACVMAL},
    MRCLASS = {11F32 (05A10 11B65 11F52 11G09)},
    DOI = {10.1007/s00013-012-0423-x},
    URL = {http://dx.doi.org/10.1007/s00013-012-0423-x},
    }
  • [DOI] M. A. Abdelraheem, M. {AA}gren, P. Beelen, and G. Leander, “On the distribution of linear biases: three instructive examples,” in Advances in cryptology–-CRYPTO 2012, Springer, Heidelberg, 2012, vol. 7417, p. 50–67.
    [Bibtex]
    @incollection {MR3005962,
    AUTHOR = {Abdelraheem, Mohamed Ahmed and {\AA}gren, Martin and Beelen,
    Peter and Leander, Gregor},
    TITLE = {On the distribution of linear biases: three instructive
    examples},
    BOOKTITLE = {Advances in cryptology---{CRYPTO} 2012},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {7417},
    PAGES = {50--67},
    PUBLISHER = {Springer, Heidelberg},
    YEAR = {2012},
    MRCLASS = {94A60},
    DOI = {10.1007/978-3-642-32009-5_4},
    URL = {http://dx.doi.org/10.1007/978-3-642-32009-5_4},
    }
  • [DOI] P. Beelen, S. R. Ghorpade, and T. H{o}holdt, “Duals of affine Grassmann codes and their relatives,” IEEE Trans. Inform. Theory, vol. 58, iss. 6, p. 3843–3855, 2012.
    [Bibtex]
    @article {MR2924405,
    AUTHOR = {Beelen, Peter and Ghorpade, Sudhir R. and H{\o}holdt, Tom},
    TITLE = {Duals of affine {G}rassmann codes and their relatives},
    JOURNAL = {IEEE Trans. Inform. Theory},
    FJOURNAL = {Institute of Electrical and Electronics Engineers.
    Transactions on Information Theory},
    VOLUME = {58},
    YEAR = {2012},
    NUMBER = {6},
    PAGES = {3843--3855},
    ISSN = {0018-9448},
    CODEN = {IETTAW},
    MRCLASS = {94B27},
    DOI = {10.1109/TIT.2012.2187171},
    URL = {http://dx.doi.org/10.1109/TIT.2012.2187171},
    }
  • [DOI] A. Bassa and P. Beelen, “The Galois closure of Drinfeld modular towers,” J. Number Theory, vol. 131, iss. 3, p. 561–577, 2011.
    [Bibtex]
    @article {MR2747158,
    AUTHOR = {Bassa, Alp and Beelen, Peter},
    TITLE = {The {G}alois closure of {D}rinfeld modular towers},
    JOURNAL = {J. Number Theory},
    FJOURNAL = {Journal of Number Theory},
    VOLUME = {131},
    YEAR = {2011},
    NUMBER = {3},
    PAGES = {561--577},
    ISSN = {0022-314X},
    CODEN = {JNUTA9},
    MRCLASS = {11G09 (11R58)},
    DOI = {10.1016/j.jnt.2010.10.006},
    URL = {http://dx.doi.org/10.1016/j.jnt.2010.10.006},
    }
  • [DOI] A. Bassa and P. Beelen, “A proof of a conjecture by Schweizer on the Drinfeld modular polynomial $\Phi_T(X,Y)$,” J. Number Theory, vol. 131, iss. 7, p. 1276–1285, 2011.
    [Bibtex]
    @article {MR2782841,
    AUTHOR = {Bassa, Alp and Beelen, Peter},
    TITLE = {A proof of a conjecture by {S}chweizer on the {D}rinfeld
    modular polynomial {$\Phi_T(X,Y)$}},
    JOURNAL = {J. Number Theory},
    FJOURNAL = {Journal of Number Theory},
    VOLUME = {131},
    YEAR = {2011},
    NUMBER = {7},
    PAGES = {1276--1285},
    ISSN = {0022-314X},
    CODEN = {JNUTA9},
    MRCLASS = {11G09 (11F52)},
    DOI = {10.1016/j.jnt.2011.01.007},
    URL = {http://dx.doi.org/10.1016/j.jnt.2011.01.007},
    }
  • [DOI] P. Beelen, S. R. Ghorpade, and T. H{o}holdt, “Affine Grassmann codes,” IEEE Trans. Inform. Theory, vol. 56, iss. 7, p. 3166–3176, 2010.
    [Bibtex]
    @article {MR2798982,
    AUTHOR = {Beelen, Peter and Ghorpade, Sudhir R. and H{\o}holdt, Tom},
    TITLE = {Affine {G}rassmann codes},
    JOURNAL = {IEEE Trans. Inform. Theory},
    FJOURNAL = {Institute of Electrical and Electronics Engineers.
    Transactions on Information Theory},
    VOLUME = {56},
    YEAR = {2010},
    NUMBER = {7},
    PAGES = {3166--3176},
    ISSN = {0018-9448},
    CODEN = {IETTAW},
    MRCLASS = {94B05 (11T06 11T71 94B27)},
    DOI = {10.1109/TIT.2010.2048470},
    URL = {http://dx.doi.org/10.1109/TIT.2010.2048470},
    }
  • [DOI] P. Beelen and K. Brander, “Key equations for list decoding of Reed-Solomon codes and how to solve them,” J. Symbolic Comput., vol. 45, iss. 7, p. 773–786, 2010.
    [Bibtex]
    @article {MR2645977,
    AUTHOR = {Beelen, Peter and Brander, Kristian},
    TITLE = {Key equations for list decoding of {R}eed-{S}olomon codes and
    how to solve them},
    JOURNAL = {J. Symbolic Comput.},
    FJOURNAL = {Journal of Symbolic Computation},
    VOLUME = {45},
    YEAR = {2010},
    NUMBER = {7},
    PAGES = {773--786},
    ISSN = {0747-7171},
    MRCLASS = {94B35},
    DOI = {10.1016/j.jsc.2010.03.010},
    URL = {http://dx.doi.org/10.1016/j.jsc.2010.03.010},
    }
  • J. S. R. Nielsen, “List decoding of Error-Correcting Codes,” Master Thesis, 2010.
    [Bibtex]
    @mastersthesis{nielsen_list_2010,
    title = {List decoding of {Error}-{Correcting} {Codes}},
    url = {http://jsrn.dk/publications.html#2010-msc},
    school = {Technical University of Denmark, Denmark},
    author = {Nielsen, Johan S. R.},
    year = {2010},
    file = {Nielsen - 2010 - List decoding of Error-Correcting Codes.pdf:/home/jsrn/media/zotero/storage/KT556AGM/Nielsen - 2010 - List decoding of Error-Correcting Codes.pdf:application/pdf}
    }
  • [DOI] A. Bassa and P. Beelen, “The Hasse-Witt invariant in some towers of function fields over finite fields,” Bull. Braz. Math. Soc. (N.S.), vol. 41, iss. 4, p. 567–582, 2010.
    [Bibtex]
    @article {MR2737317,
    AUTHOR = {Bassa, A. and Beelen, P.},
    TITLE = {The {H}asse-{W}itt invariant in some towers of function fields
    over finite fields},
    JOURNAL = {Bull. Braz. Math. Soc. (N.S.)},
    FJOURNAL = {Bulletin of the Brazilian Mathematical Society. New Series.
    Boletim da Sociedade Brasileira de Matem\'atica},
    VOLUME = {41},
    YEAR = {2010},
    NUMBER = {4},
    PAGES = {567--582},
    ISSN = {1678-7544},
    MRCLASS = {14H05 (11G20 14G15)},
    DOI = {10.1007/s00574-010-0026-8},
    URL = {http://dx.doi.org/10.1007/s00574-010-0026-8},
    }
  • [DOI] P. Beelen and K. Brander, “Efficient list decoding of a class of algebraic-geometry codes,” Adv. Math. Commun., vol. 4, iss. 4, p. 485–518, 2010.
    [Bibtex]
    @article {MR2734040,
    AUTHOR = {Beelen, Peter and Brander, Kristian},
    TITLE = {Efficient list decoding of a class of algebraic-geometry
    codes},
    JOURNAL = {Adv. Math. Commun.},
    FJOURNAL = {Advances in Mathematics of Communications},
    VOLUME = {4},
    YEAR = {2010},
    NUMBER = {4},
    PAGES = {485--518},
    ISSN = {1930-5346},
    MRCLASS = {94B35 (11T71 14G50 94B27)},
    DOI = {10.3934/amc.2010.4.485},
    URL = {http://dx.doi.org/10.3934/amc.2010.4.485},
    }
  • P. Beelen and G. Leander, “Reconstruction of highly non linear sboxes from linear codes,” in Enhancing cryptographic primitives with techniques from error correcting codes, IOS, Amsterdam, 2009, vol. 23, p. 153–159.
    [Bibtex]
    @incollection {MR2762234,
    AUTHOR = {Beelen, Peter and Leander, Gregor},
    TITLE = {Reconstruction of highly non linear sboxes from linear codes},
    BOOKTITLE = {Enhancing cryptographic primitives with techniques from error
    correcting codes},
    SERIES = {NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur.},
    VOLUME = {23},
    PAGES = {153--159},
    PUBLISHER = {IOS, Amsterdam},
    YEAR = {2009},
    MRCLASS = {94B05 (06E30 94C10)},
    }
  • [DOI] P. Beelen, “A generalization of Baker’s theorem,” Finite Fields Appl., vol. 15, iss. 5, p. 558–568, 2009.
    [Bibtex]
    @article {MR2554039,
    AUTHOR = {Beelen, Peter},
    TITLE = {A generalization of {B}aker's theorem},
    JOURNAL = {Finite Fields Appl.},
    FJOURNAL = {Finite Fields and their Applications},
    VOLUME = {15},
    YEAR = {2009},
    NUMBER = {5},
    PAGES = {558--568},
    ISSN = {1071-5797},
    MRCLASS = {14H05},
    DOI = {10.1016/j.ffa.2009.04.003},
    URL = {http://dx.doi.org/10.1016/j.ffa.2009.04.003},
    }
  • [DOI] A. Bassa and P. Beelen, “On the construction of Galois towers,” in Arithmetic, geometry, cryptography and coding theory, Amer. Math. Soc., Providence, RI, 2009, vol. 487, p. 9–20.
    [Bibtex]
    @incollection {MR2555984,
    AUTHOR = {Bassa, Alp and Beelen, Peter},
    TITLE = {On the construction of {G}alois towers},
    BOOKTITLE = {Arithmetic, geometry, cryptography and coding theory},
    SERIES = {Contemp. Math.},
    VOLUME = {487},
    PAGES = {9--20},
    PUBLISHER = {Amer. Math. Soc., Providence, RI},
    YEAR = {2009},
    MRCLASS = {14G32 (11R58 14H05)},
    DOI = {10.1090/conm/487/09522},
    URL = {http://dx.doi.org/10.1090/conm/487/09522},
    }
  • [DOI] P. Beelen and D. Ruano, “The order bound for toric codes,” in Applied algebra, algebraic algorithms, and error-correcting codes, Springer, Berlin, 2009, vol. 5527, p. 1–10.
    [Bibtex]
    @incollection {MR2580848,
    AUTHOR = {Beelen, Peter and Ruano, Diego},
    TITLE = {The order bound for toric codes},
    BOOKTITLE = {Applied algebra, algebraic algorithms, and error-correcting
    codes},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {5527},
    PAGES = {1--10},
    PUBLISHER = {Springer, Berlin},
    YEAR = {2009},
    MRCLASS = {94B27 (14G50)},
    DOI = {10.1007/978-3-642-02181-7_1},
    URL = {http://dx.doi.org/10.1007/978-3-642-02181-7_1},
    }
  • [DOI] P. Beelen and T. H{o}holdt, “List decoding using syndromes,” in Algebraic geometry and its applications, World Sci. Publ., Hackensack, NJ, 2008, vol. 5, p. 315–331.
    [Bibtex]
    @incollection {MR2484061,
    AUTHOR = {Beelen, Peter and H{\o}holdt, Tom},
    TITLE = {List decoding using syndromes},
    BOOKTITLE = {Algebraic geometry and its applications},
    SERIES = {Ser. Number Theory Appl.},
    VOLUME = {5},
    PAGES = {315--331},
    PUBLISHER = {World Sci. Publ., Hackensack, NJ},
    YEAR = {2008},
    MRCLASS = {94B35 (14G50)},
    DOI = {10.1142/9789812793430_0016},
    URL = {http://dx.doi.org/10.1142/9789812793430_0016},
    }
  • [DOI] P. Beelen and T. H{o}holdt, “The decoding of algebraic geometry codes,” in Advances in algebraic geometry codes, World Sci. Publ., Hackensack, NJ, 2008, vol. 5, p. 49–98.
    [Bibtex]
    @incollection {MR2509121,
    AUTHOR = {Beelen, Peter and H{\o}holdt, Tom},
    TITLE = {The decoding of algebraic geometry codes},
    BOOKTITLE = {Advances in algebraic geometry codes},
    SERIES = {Ser. Coding Theory Cryptol.},
    VOLUME = {5},
    PAGES = {49--98},
    PUBLISHER = {World Sci. Publ., Hackensack, NJ},
    YEAR = {2008},
    MRCLASS = {94B27 (14G50 94-02 94B35)},
    DOI = {10.1142/9789812794017_0002},
    URL = {http://dx.doi.org/10.1142/9789812794017_0002},
    }
  • [DOI] P. Beelen, “The order bound for general algebraic geometric codes,” Finite Fields Appl., vol. 13, iss. 3, p. 665–680, 2007.
    [Bibtex]
    @article {MR2332494,
    AUTHOR = {Beelen, Peter},
    TITLE = {The order bound for general algebraic geometric codes},
    JOURNAL = {Finite Fields Appl.},
    FJOURNAL = {Finite Fields and their Applications},
    VOLUME = {13},
    YEAR = {2007},
    NUMBER = {3},
    PAGES = {665--680},
    ISSN = {1071-5797},
    MRCLASS = {94B27 (11T71)},
    DOI = {10.1016/j.ffa.2006.09.006},
    URL = {http://dx.doi.org/10.1016/j.ffa.2006.09.006},
    }
  • [DOI] P. Beelen and N. Tuta{c{s}}, “A generalization of the Weierstrass semigroup,” J. Pure Appl. Algebra, vol. 207, iss. 2, p. 243–260, 2006.
    [Bibtex]
    @article {MR2254885,
    AUTHOR = {Beelen, Peter and Tuta{\c{s}}, Nesrin},
    TITLE = {A generalization of the {W}eierstrass semigroup},
    JOURNAL = {J. Pure Appl. Algebra},
    FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {207},
    YEAR = {2006},
    NUMBER = {2},
    PAGES = {243--260},
    ISSN = {0022-4049},
    CODEN = {JPAAA2},
    MRCLASS = {14H55 (14G15 14G50 94B27)},
    DOI = {10.1016/j.jpaa.2005.09.017},
    URL = {http://dx.doi.org/10.1016/j.jpaa.2005.09.017},
    }
  • [DOI] P. Beelen, A. Garcia, and H. Stichtenoth, “Towards a classification of recursive towers of function fields over finite fields,” Finite Fields Appl., vol. 12, iss. 1, p. 56–77, 2006.
    [Bibtex]
    @article {MR2190187,
    AUTHOR = {Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning},
    TITLE = {Towards a classification of recursive towers of function
    fields over finite fields},
    JOURNAL = {Finite Fields Appl.},
    FJOURNAL = {Finite Fields and their Applications},
    VOLUME = {12},
    YEAR = {2006},
    NUMBER = {1},
    PAGES = {56--77},
    ISSN = {1071-5797},
    MRCLASS = {11R58},
    DOI = {10.1016/j.ffa.2005.01.004},
    URL = {http://dx.doi.org/10.1016/j.ffa.2005.01.004},
    }
  • P. Beelen, A. Garcia, and H. Stichtenoth, “On towers of function fields over finite fields,” in Arithmetic, geometry and coding theory (AGCT 2003), Soc. Math. France, Paris, 2005, vol. 11, p. 1–20.
    [Bibtex]
    @incollection {MR2182834,
    AUTHOR = {Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning},
    TITLE = {On towers of function fields over finite fields},
    BOOKTITLE = {Arithmetic, geometry and coding theory ({AGCT} 2003)},
    SERIES = {S\'emin. Congr.},
    VOLUME = {11},
    PAGES = {1--20},
    PUBLISHER = {Soc. Math. France, Paris},
    YEAR = {2005},
    MRCLASS = {11R58 (11G20)},
    }
  • P. Beelen, A. Garcia, and H. Stichtenoth, “On ramification and genus of recursive towers,” Port. Math. (N.S.), vol. 62, iss. 2, p. 231–243, 2005.
    [Bibtex]
    @article {MR2147451,
    AUTHOR = {Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning},
    TITLE = {On ramification and genus of recursive towers},
    JOURNAL = {Port. Math. (N.S.)},
    FJOURNAL = {Portugaliae Mathematica. Nova S\'erie},
    VOLUME = {62},
    YEAR = {2005},
    NUMBER = {2},
    PAGES = {231--243},
    ISSN = {0032-5155},
    MRCLASS = {14G15 (14H05)},
    }
  • [DOI] P. Beelen and I. I. Bouw, “Asymptotically good towers and differential equations,” Compos. Math., vol. 141, iss. 6, p. 1405–1424, 2005.
    [Bibtex]
    @article {MR2188442,
    AUTHOR = {Beelen, Peter and Bouw, Irene I.},
    TITLE = {Asymptotically good towers and differential equations},
    JOURNAL = {Compos. Math.},
    FJOURNAL = {Compositio Mathematica},
    VOLUME = {141},
    YEAR = {2005},
    NUMBER = {6},
    PAGES = {1405--1424},
    ISSN = {0010-437X},
    MRCLASS = {11G20 (14G05 14G15)},
    DOI = {10.1112/S0010437X05001624},
    URL = {http://dx.doi.org/10.1112/S0010437X05001624},
    }
  • [DOI] P. Beelen, “Graphs and recursively defined towers of function fields,” J. Number Theory, vol. 108, iss. 2, p. 217–240, 2004.
    [Bibtex]
    @article {MR2098637,
    AUTHOR = {Beelen, Peter},
    TITLE = {Graphs and recursively defined towers of function fields},
    JOURNAL = {J. Number Theory},
    FJOURNAL = {Journal of Number Theory},
    VOLUME = {108},
    YEAR = {2004},
    NUMBER = {2},
    PAGES = {217--240},
    ISSN = {0022-314X},
    CODEN = {JNUTA9},
    MRCLASS = {11R58},
    DOI = {10.1016/j.jnt.2004.05.011},
    URL = {http://dx.doi.org/10.1016/j.jnt.2004.05.011},
    }
  • [DOI] P. Beelen, A. Garcia, and H. Stichtenoth, “On towers of function fields of Artin-Schreier type,” Bull. Braz. Math. Soc. (N.S.), vol. 35, iss. 2, p. 151–164, 2004.
    [Bibtex]
    @article {MR2081020,
    AUTHOR = {Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning},
    TITLE = {On towers of function fields of {A}rtin-{S}chreier type},
    JOURNAL = {Bull. Braz. Math. Soc. (N.S.)},
    FJOURNAL = {Bulletin of the Brazilian Mathematical Society. New Series.
    Boletim da Sociedade Brasileira de Matem\'atica},
    VOLUME = {35},
    YEAR = {2004},
    NUMBER = {2},
    PAGES = {151--164},
    ISSN = {1678-7544},
    MRCLASS = {11R58 (11D59 14G15 14H05)},
    DOI = {10.1007/s00574-004-0008-9},
    URL = {http://dx.doi.org/10.1007/s00574-004-0008-9},
    }
  • [DOI] P. Beelen and R. Gramlich, “On anti-automorphisms of the first kind in division rings,” Proc. Amer. Math. Soc., vol. 130, iss. 12, p. 3745–3746, 2002.
    [Bibtex]
    @article {MR1920057,
    AUTHOR = {Beelen, Peter and Gramlich, Ralf},
    TITLE = {On anti-automorphisms of the first kind in division rings},
    JOURNAL = {Proc. Amer. Math. Soc.},
    FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {130},
    YEAR = {2002},
    NUMBER = {12},
    PAGES = {3745--3746},
    ISSN = {0002-9939},
    CODEN = {PAMYAR},
    MRCLASS = {16K20},
    DOI = {10.1090/S0002-9939-02-06746-1},
    URL = {http://dx.doi.org/10.1090/S0002-9939-02-06746-1},
    }
  • P. H. T. Beelen and J. M. Doumen, “Pseudorandom sequences from elliptic curves,” in Finite fields with applications to coding theory, cryptography and related areas (Oaxaca, 2001), Springer, Berlin, 2002, p. 37–52.
    [Bibtex]
    @incollection {MR1995326,
    AUTHOR = {Beelen, P. H. T. and Doumen, J. M.},
    TITLE = {Pseudorandom sequences from elliptic curves},
    BOOKTITLE = {Finite fields with applications to coding theory, cryptography
    and related areas ({O}axaca, 2001)},
    PAGES = {37--52},
    PUBLISHER = {Springer, Berlin},
    YEAR = {2002},
    MRCLASS = {11K45 (11G05 11L40)},
    }
  • [DOI] P. Beelen and R. Pellikaan, “The Newton polygon of plane curves with many rational points,” Des. Codes Cryptogr., vol. 21, iss. 1-3, p. 41–67, 2000.
    [Bibtex]
    @article {MR1801161,
    AUTHOR = {Beelen, Peter and Pellikaan, Ruud},
    TITLE = {The {N}ewton polygon of plane curves with many rational
    points},
    NOTE = {Special issue dedicated to Dr. Jaap Seidel on the occasion of
    his 80th birthday (Oisterwijk, 1999)},
    JOURNAL = {Des. Codes Cryptogr.},
    FJOURNAL = {Designs, Codes and Cryptography. An International Journal},
    VOLUME = {21},
    YEAR = {2000},
    NUMBER = {1-3},
    PAGES = {41--67},
    ISSN = {0925-1022},
    CODEN = {DCCREC},
    MRCLASS = {14G15 (14G50 14H50)},
    DOI = {10.1023/A:1008323208670},
    URL = {http://dx.doi.org/10.1023/A:1008323208670},
    }