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

- J. S. R. Nielsen and A. Storjohann, “Algorithms for Simultaneous Padé Approximations,” in International Symposium on Symbolic and Algebraic Computation, 2016.

[Bibtex]`@inproceedings{nielsen_algorithms_2016, title = {Algorithms for {Simultaneous} {Padé} {Approximations}}, url = {http://arxiv.org/abs/1602.00836}, abstract = {We describe how to solve simultaneous Pad{\textbackslash}'e approximations over a power series ring \$K[[x]]\$ for a field \$K\$ using \$O{\textasciitilde}(n{\textasciicircum}\{{\textbackslash}omega - 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 and with different advantages. Both algorithms return reduced bases for the complete set of solutions to the input approximation problem. Our results are made possible by recent breakthroughs in fast computations of minimal approximant bases and Hermite Pad{\textbackslash}'e approximations.}, urldate = {2016-03-06}, booktitle = {International {Symposium} on {Symbolic} and {Algebraic} {Computation}}, author = {Nielsen, Johan S. R. and Storjohann, Arne}, month = feb, year = {2016}, note = {Submitted}, keywords = {Computer Science - Symbolic Computation}, file = {arXiv\:1602.00836 PDF:/home/jsrn/media/zotero/storage/2XK4NRCC/Nielsen and Storjohann - 2016 - Algorithms for Simultaneous Pad'e Approximations.pdf:application/pdf} }`

- J. S. R. Nielsen, “Power Decoding of Reed–Solomon Up to the Johnson Radius,” Preprint, 2016.

[Bibtex]`@article{nielsen_power_2016, title = {Power {Decoding} of {Reed}–{Solomon} {Up} to the {Johnson} {Radius}}, url = {http://jsrn.dk/publications.html#2015-ieee-powermults}, journal = {Preprint}, author = {Nielsen, Johan S. R.}, month = jan, year = {2016} }`

- S. Puchinger, J. S. R. Nielsen, W. Li, and V. Sidorenko, “Row Reduction Applied to Decoding of Rank Metric and Subspace Codes,” Designs, Codes and Cryptography, 2016.

[Bibtex]`@article{puchinger_row_2016, title = {Row {Reduction} {Applied} to {Decoding} of {Rank} {Metric} and {Subspace} {Codes}}, url = {http://arxiv.org/abs/1510.04728}, journal = {Designs, Codes and Cryptography}, author = {Puchinger, Sven and Nielsen, Johan S. R. and Li, Wenhui and Sidorenko, Vladimir}, month = feb, year = {2016}, note = {Submitted}, keywords = {Computer Science - Information Theory} }`

- 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, pp. 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}, }`

- 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} }`

- A. Bassa, P. Beelen, and N. Nguyen, “Good families of Drinfeld modular curves,” LMS J. Comput. Math., vol. 18, iss. 1, pp. 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}, }`

- 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)}, }`

- J. S. R. Nielsen and P. Beelen, “Sub-quadratic decoding of one-point Hermitian codes,” IEEE Trans. Inform. Theory, vol. 61, iss. 6, pp. 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}, }`

- P. Beelen, S. R. Ghorpade, and S. U. Hasan, “Linear codes associated to determinantal varieties,” Discrete Math., vol. 338, iss. 8, pp. 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}, }`

- 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, A. Garcia, and H. Stichtenoth, “An improvement of the Gilbert-Varshamov bound over nonprime fields,” IEEE Trans. Inform. Theory, vol. 60, iss. 7, pp. 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, “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} }`

- 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, “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} }`

- 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 = {68P30, 94B35, Coding and Information Theory, Combinatorics, Data Encryption, Data Structures, Cryptology and Information Theory, Discrete Mathematics in Computer Science, Guruswami–Sudan, Information and Communication, Circuits, list decoding, Multi-trial, Reed–Solomon codes, Re-encoding transformation}, 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} }`

- A. Bassa, P. Beelen, and N. Nguyen, “Good towers of function fields,” in Algebraic curves and finite fields, De Gruyter, Berlin, 2014, vol. 16, pp. 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)}, }`

- A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth, “Galois towers over non-prime finite fields,” Acta Arith., vol. 164, iss. 2, pp. 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}, }`

- 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} }`

- 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} }`

- 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, pp. 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}, }`

- J. S. R. Nielsen, “Generalised Multi-sequence Shift-Register Synthesis using Module Minimisation,” in IEEE International Symposium on Information Theory, 2013, pp. 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} }`

- 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, pp. 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}, }`

- 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, pp. 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}, }`

- J. S. R. Nielsen, “List Decoding of Algebraic Codes,” PhD Thesis, 2013.

[Bibtex]`@phdthesis{nielsen_list_2013, 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} }`

- 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} }`

- 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, pp. 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}, }`

- 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, pp. 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}, }`

- H. Aref, P. Beelen, and M. Br{o}ns, “Bilinear relative equilibria of identical point vortices,” J. Nonlinear Sci., vol. 22, iss. 5, pp. 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}, }`

- 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, pp. 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}, }`

- P. Beelen and G. Leander, “A new construction of highly nonlinear S-boxes,” Cryptogr. Commun., vol. 4, iss. 1, pp. 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}, }`

- 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, pp. 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}, }`

- A. Bassa and P. Beelen, “The Galois closure of Drinfeld modular towers,” J. Number Theory, vol. 131, iss. 3, pp. 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}, }`

- J. S. R. Nielsen, “List decoding of Error-Correcting Codes,” PhD Thesis, 2010.

[Bibtex]`@phdthesis{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} }`

- P. Beelen and K. Brander, “Efficient list decoding of a class of algebraic-geometry codes,” Adv. Math. Commun., vol. 4, iss. 4, pp. 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}, }`

- 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, pp. 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}, }`

- P. Beelen, S. R. Ghorpade, and T. H{o}holdt, “Affine Grassmann codes,” IEEE Trans. Inform. Theory, vol. 56, iss. 7, pp. 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}, }`

- 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, pp. 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}, }`

- 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, pp. 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)}, }`

- 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, pp. 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}, }`

- 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, pp. 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}, }`

- P. Beelen, “A generalization of Baker’s theorem,” Finite Fields Appl., vol. 15, iss. 5, pp. 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}, }`

- 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, pp. 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}, }`

- 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, pp. 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}, }`

- P. Beelen, “The order bound for general algebraic geometric codes,” Finite Fields Appl., vol. 13, iss. 3, pp. 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}, }`

- 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, pp. 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 and N. Tuta{c{s}}, “A generalization of the Weierstrass semigroup,” J. Pure Appl. Algebra, vol. 207, iss. 2, pp. 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}, }`

- P. Beelen and I. I. Bouw, “Asymptotically good towers and differential equations,” Compos. Math., vol. 141, iss. 6, pp. 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}, }`

- 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, pp. 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, pp. 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)}, }`

- P. Beelen, “Graphs and recursively defined towers of function fields,” J. Number Theory, vol. 108, iss. 2, pp. 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}, }`

- 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, pp. 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}, }`

- P. Beelen and R. Gramlich, “On anti-automorphisms of the first kind in division rings,” Proc. Amer. Math. Soc., vol. 130, iss. 12, pp. 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, pp. 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)}, }`

- P. Beelen and R. Pellikaan, “The Newton polygon of plane curves with many rational points,” Des. Codes Cryptogr., vol. 21, iss. 1-3, pp. 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}, }`