Research

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

69 entries « 1 of 2 »

2018

Barelli, É; Beelen, P; Datta, M; Neiger, V; Rosenkilde, J

Two-Point Codes for the Generalized GK Curve Journal Article

IEEE Transactions on Information Theory, 64 (9), pp. 6268–6276, 2018, ISSN: 0018-9448.

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Neiger, Vincent; Rosenkilde, Johan; Solomatov, Grigory

Computing Popov and Hermite forms of rectangular polynomial matrices Inproceedings

International Symposium in Symbolic and Algebraic Computation, 2018.

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Rosenkilde, Johan

Power Decoding of Reed–Solomon Up to the Johnson Radius Journal Article

Advances in Mathematics of Communications, 12 (1), pp. 81–106, 2018.

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Beelen, Peter; Bossert, Martin; Puchinger, Sven; Rosenkilde, Johan

Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography Inproceedings

IEEE International Symposium on Information Theory, 2018.

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2017

Puchinger, S; Rosenkilde, Johan

Decoding of interleaved Reed-Solomon codes using improved power decoding Inproceedings

IEEE International Symposium on Information Theory, pp. 356–360, 2017.

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Beelen, P; Puchinger, S; Rosenkilde, Johan

Twisted Reed-Solomon Codes Inproceedings

IEEE International Symposium on Information Theory (ISIT), pp. 336–340, 2017.

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Puchinger, Sven; Rosenkilde, Johan; Li, Wenhui; Sidorenko, Vladimir

Row reduction applied to decoding of rank-metric and subspace codes Journal Article

Designs, Codes and Cryptography, 82 (1-2), pp. 389–409, 2017, ISSN: 0925-1022, 1573-7586.

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Neiger, Vincent; Rosenkilde, Johan; Schost, Éric

Fast Computation of the Roots of Polynomials Over the Ring of Power Series Inproceedings

International Symposium on Symbolic and Algebraic Computation, 2017.

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Puchinger, Sven; Rosenkilde, Johan; Sheekey, John

Further Generalisations of Twisted Gabidulin Codes Inproceedings

International Workshop in Coding Theory and Cryptography, 2017.

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Khochtali, Mohamed; Rosenkilde, Johan; Storjohann, Arne

Popov form computation for matrices of Ore polynomials Inproceedings

International Symposium on Symbolic and Algebraic Computation, pp. 253–260, The Association for Computing Machinery, 2017, ISBN: 978-1-4503-5064-8.

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Puchinger, Sven; Rosenkilde, Johan; Bouw, Irene

Improved Power Decoding of One-Point Hermitian Codes Inproceedings

International Workshop in Coding Theory and Cryptography, 2017.

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2016

Rosenkilde, Johan; Storjohann, Arne

Algorithms for Simultaneous Padé Approximations Inproceedings

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, pp. 405–412, ACM, New York, NY, USA, 2016, ISBN: 978-1-4503-4380-0.

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Puchinger, Sven; Müelich, Sven; Mödinger, David; Rosenkilde, Johan; Bossert, Martin

Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm Inproceedings

International Workshop in Algebraic and Combinatorial Coding Theory, 2016, (arXiv: 1604.05899).

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2015

Nielsen, J S R; Beelen, P

Sub-Quadratic Decoding of One-Point Hermitian Codes Journal Article

IEEE Transactions on Information Theory, 61 (6), pp. 3225–3240, 2015, ISSN: 0018-9448.

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Bassa, Alp; Beelen, Peter; Nguyen, Nhut

Good families of Đrinfeld modular curves Journal Article

LMS J. Comput. Math., 18 (1), pp. 699–712, 2015, ISSN: 1461-1570.

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Bassa, Alp; Beelen, Peter; Garcia, Arnaldo; Stichtenoth, Henning

Towers of function fields over non-prime finite fields Journal Article

Mosc. Math. J., 15 (1), pp. 1–29, 181, 2015, ISSN: 1609-3321.

BibTeX

Abdelraheem, Mohamed Ahmed; Beelen, Peter; Bogdanov, Andrey; Tischhauser, Elmar

Twisted polynomials and forgery attacks on GCM Incollection

Advances in cryptology---EUROCRYPT 2015. Part I, 9056 , pp. 762–786, Springer, Heidelberg, 2015.

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Nielsen, Johan S R; Beelen, Peter

Sub-quadratic decoding of one-point Ħermitian codes Journal Article

IEEE Trans. Inform. Theory, 61 (6), pp. 3225–3240, 2015, ISSN: 0018-9448.

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Beelen, Peter; Ghorpade, Sudhir R; Hasan, Sartaj Ul

Linear codes associated to determinantal varieties Journal Article

Discrete Math., 338 (8), pp. 1493–1500, 2015, ISSN: 0012-365X.

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Li, Wenhui; Nielsen, Johan S R; Puchinger, Sven; Sidorenko, Vladimir

Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation Inproceedings

International Workshop on Coding and Cryptography, 2015, (arXiv: 1501.04797).

Abstract | Links | BibTeX

2014

Nielsen, Johan S R

Power Decoding of Reed–Solomon Up to the Johnson Radius Inproceedings

International Workshop on Algebraic and Combinatorial Coding Theory, 2014.

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Bassa, Alp; Beelen, Peter; Nguyen, Nhut

Good towers of function fields Incollection

Algebraic curves and finite fields, 16 , pp. 23–40, De Gruyter, Berlin, 2014.

BibTeX

Bassa, Alp; Beelen, Peter; Garcia, Arnaldo; Stichtenoth, Henning

Galois towers over non-prime finite fields Journal Article

Acta Arith., 164 (2), pp. 163–179, 2014, ISSN: 0065-1036.

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Bassa, Alp; Beelen, Peter; Garcia, Arnaldo; Stichtenoth, Henning

An improvement of the Gilbert-Varshamov bound over nonprime fields Journal Article

IEEE Trans. Inform. Theory, 60 (7), pp. 3859–3861, 2014, ISSN: 0018-9448.

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Mohamed, Mostafa H; Nielsen, Johan S R; Bossert, Martin

Reduced List Decoding of Reed–Solomon Codes Using Reliability Information Inproceedings

International Symposium on Mathematical Theory of Networks and Systems, 2014.

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Nielsen, Johan S R; Zeh, Alexander

Multi-Trial Guruswami–Sudan Decoding for Generalised Reed–Solomon Codes Journal Article

Designs, Codes and Cryptography, (Special issue on Coding and Cryptography), 2014, ISSN: 0925-1022, 1573-7586.

Abstract | Links | BibTeX

Nielsen, Johan S R; Zeh, Alexander

Multi-Trial Guruswami–Sudan Decoding for Generalised Reed–Solomon Codes Journal Article

Designs, Codes and Cryptography, (Special issue on Coding and Cryptography), 2014, ISSN: 0925-1022, 1573-7586.

Abstract | Links | BibTeX

Nielsen, Johan S R

Power Decoding of Reed–Solomon Codes Revisited Inproceedings

International Castle Meeting on Coding Theory and Applications, 2014.

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Nielsen, Johan S R

Solving generalised Padé approximations over polynomial rings Inproceedings

Preprint, 2014, (Available at http://jsrn.dk/).

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Nielsen, Johan S R; Zeh, Alexander

Multi-Trial Guruswami–Sudan Decoding for Generalised Reed–Solomon Codes Journal Article

Designs, Codes and Cryptography, (Special issue on Coding and Cryptography), 2014, ISSN: 0925-1022, 1573-7586.

Abstract | Links | BibTeX

Nielsen, J S R

Fast Kötter-Nielsen-Høholdt Interpolation in the Guruswami-Sudan Algorithm Inproceedings

2014.

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2013

Beelen, Peter

Affine Grassmann codes: an overview Incollection

From modern coding theory to postmodern coding theory (Japanese), 44 , pp. 77–85, Kyushu Univ. Fac. Math., Fukuoka, 2013.

BibTeX

Beelen, Peter; Høholdt, Tom; Nielsen, Johan S R; Wu, Yingquan

On rational interpolation-based list-decoding and list-decoding binary Goppa codes Journal Article

IEEE Trans. Inform. Theory, 59 (6), pp. 3269–3281, 2013, ISSN: 0018-9448.

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Beelen, Peter; Ruano, Diego

Bounding the number of points on a curve using a generalization of Weierstrass semigroups Journal Article

Des. Codes Cryptogr., 66 (1-3), pp. 221–230, 2013, ISSN: 0925-1022.

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Nielsen, Johan S R

Monkeys Inproceedings

Hello, 2013.

BibTeX

Beelen, Peter; Høholdt, Tom; Nielsen, Johan S R; Wu, Yingquan

On Rational Interpolation-Based List-Decoding and List-Decoding Binary Goppa Codes Journal Article

IEEE Transactions on Information Theory, 59 (6), pp. 3269–3281, 2013, ISSN: 0018-9448, 1557-9654.

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Nielsen, Johan S R

List Decoding of Algebraic Codes PhD Thesis

Technical University of Denmark, 2013.

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Nielsen, Johan S R; Zeh, Alexander

Multi-Trial Guruswami--Sudan Decoding for Generalised Reed--Solomon Codes Inproceedings

International Workshop on Coding and Cryptography, 2013.

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Nielsen, Johan S R

Generalised Multi-sequence Shift-Register Synthesis using Module Minimisation Inproceedings

IEEE International Symposium on Information Theory, pp. 882–886, 2013.

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Li, W; Sidorenko, V; Nielsen, Johan S R

On Decoding Interleaved Chinese Remainder Codes Inproceedings

IEEE International Symposium on Information Theory, 2013.

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2012

Abdelraheem, Mohamed Ahmed; Ågren, Martin; Beelen, Peter; Leander, Gregor

On the distribution of linear biases: three instructive examples Incollection

Advances in cryptology---CRYPTO 2012, 7417 , pp. 50–67, Springer, Heidelberg, 2012.

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Aref, H; Beelen, P; Brøns, M

Bilinear relative equilibria of identical point vortices Journal Article

J. Nonlinear Sci., 22 (5), pp. 849–885, 2012, ISSN: 0938-8974.

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Bassa, Alp; Beelen, Peter

A closed-form expression for the Đrinfeld modular polynomial $Phi_T(X,Y)$ Journal Article

Arch. Math. (Basel), 99 (3), pp. 237–245, 2012, ISSN: 0003-889X.

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Beelen, Peter; Ghorpade, Sudhir R; Høholdt, Tom

Duals of affine Grassmann codes and their relatives Journal Article

IEEE Trans. Inform. Theory, 58 (6), pp. 3843–3855, 2012, ISSN: 0018-9448.

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Beelen, Peter; Leander, Gregor

A new construction of highly nonlinear S-boxes Journal Article

Cryptogr. Commun., 4 (1), pp. 65–77, 2012, ISSN: 1936-2447.

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2011

Bassa, Alp; Beelen, Peter

A proof of a conjecture by Schweizer on the Đrinfeld modular polynomial $Phi_T(X,Y)$ Journal Article

J. Number Theory, 131 (7), pp. 1276–1285, 2011, ISSN: 0022-314X.

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Bassa, Alp; Beelen, Peter

The Galois closure of Đrinfeld modular towers Journal Article

J. Number Theory, 131 (3), pp. 561–577, 2011, ISSN: 0022-314X.

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2010

Beelen, Peter; Ghorpade, Sudhir R; Høholdt, Tom

Affine Grassmann codes Journal Article

IEEE Trans. Inform. Theory, 56 (7), pp. 3166–3176, 2010, ISSN: 0018-9448.

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Bassa, A; Beelen, P

The Ħasse-Witt invariant in some towers of function fields over finite fields Journal Article

Bull. Braz. Math. Soc. (N.S.), 41 (4), pp. 567–582, 2010, ISSN: 1678-7544.

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Beelen, Peter; Brander, Kristian

Efficient list decoding of a class of algebraic-geometry codes Journal Article

Adv. Math. Commun., 4 (4), pp. 485–518, 2010, ISSN: 1930-5346.

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69 entries « 1 of 2 »