, Linear Diophantine Equations Over Polynomials and Soft Decoding of Reed???Solomon Codes, IEEE Transactions on Information Theory, vol.51, issue.7, pp.2257-2265, 2005.
DOI : 10.1109/TIT.2005.850097
, A reliable method for computing M-Pad?? approximants on arbitrary staircases, Journal of Computational and Applied Mathematics, vol.40, issue.1, pp.19-42, 1992.
DOI : 10.1016/0377-0427(92)90039-Z
, A Uniform Approach for the Fast Computation of Matrix-Type Pad?? Approximants, SIAM Journal on Matrix Analysis and Applications, vol.15, issue.3, pp.804-823, 1994.
DOI : 10.1137/S0895479892230031
, Key equations for list decoding of Reed???Solomon codes and how to solve them, Journal of Symbolic Computation, vol.45, issue.7, pp.773-786, 2010.
DOI : 10.1016/j.jsc.2010.03.010
, On Rational Interpolation-Based List-Decoding and List-Decoding Binary Goppa Codes, IEEE Transactions on Information Theory, vol.59, issue.6, pp.3269-3281, 2013.
DOI : 10.1109/TIT.2013.2243800
, Simplified High-Speed High-Distance List Decoding for Alternant Codes, PQCrypto'11, pp.200-216, 2011.
DOI : 10.1016/0022-314X(69)90047-X
, Asymptotically fast solution of toeplitz and related systems of linear equations, Linear Algebra and its Applications, vol.34, pp.103-116, 1980.
DOI : 10.1016/0024-3795(80)90161-5
, Solving structured linear systems with large displacement rank, Theoretical Computer Science, vol.407, issue.1-3, pp.155-181, 2008.
DOI : 10.1016/j.tcs.2008.05.014
, Interpolation and List Decoding of Algebraic Codes, 2010.
, Multivariate List Decoding of Evaluation Codes with a Gröbner Basis Perspective, 2008.
, On fast multiplication of polynomials over arbitrary algebras, Acta Informatica, vol.7, issue.7, pp.693-701, 1991.
DOI : 10.1007/BF01178683
, On the complexity of multivariate interpolation with multiplicities and of simultaneous polynomial approximations, 2012.
, Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding, Advances in Mathematics of Communications, vol.9, issue.3, pp.298-308, 2011.
DOI : 10.3934/amc.2015.9.311
, Approximate common divisors via lattices, Tenth Algorithmic Number Theory Symposium, pp.271-293
DOI : 10.2140/obs.2013.1.271
URL : http://arxiv.org/abs/1108.2714
, Matrix multiplication via arithmetic progressions, Proceedings of the nineteenth annual ACM conference on Theory of computing , STOC '87, pp.251-280, 1990.
DOI : 10.1145/28395.28396
URL : http://doi.org/10.1016/s0747-7171(08)80013-2
, A probabilistic remark on algebraic program testing, Information Processing Letters, vol.7, issue.4, pp.193-195, 1978.
DOI : 10.1016/0020-0190(78)90067-4
, A generalization of the Berlekamp-Massey algorithm for multisequence shift-register synthesis with applications to decoding cyclic codes, IEEE Transactions on Information Theory, vol.37, issue.5, pp.1274-1287, 1991.
DOI : 10.1109/18.133246
, Improved Hermite multivariate polynomial interpolation, 2006 IEEE International Symposium on Information Theory, pp.143-147, 2006.
DOI : 10.1109/ISIT.2006.261691
, Modern Computer Algebra (third edition), 2013.
, On the complexity of polynomial matrix computations, Proceedings of the 2003 international symposium on Symbolic and algebraic computation , ISSAC '03, pp.135-142, 2003.
DOI : 10.1145/860854.860889
, Triangular <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>x</mml:mi></mml:math>-basis decompositions and derandomization of linear algebra algorithms over <mml:math altimg="si2.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mstyle mathvariant="sans-serif"><mml:mi>K</mml:mi></mml:mstyle><mml:mrow><mml:mo>[</mml:mo><mml:mi>x</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:math>, Journal of Symbolic Computation, vol.47, issue.4, pp.422-453, 2012.
DOI : 10.1016/j.jsc.2011.09.006
, Explicit Codes Achieving List Decoding Capacity: Error-Correction With Optimal Redundancy, IEEE Transactions on Information Theory, vol.54, issue.1, pp.135-150, 2008.
DOI : 10.1109/TIT.2007.911222
, Improved decoding of Reed-Solomon and algebraic-geometry codes, IEEE Transactions on Information Theory, vol.45, issue.6, pp.1757-1767, 1999.
DOI : 10.1109/18.782097
, Theorie der höheren Differentiale in einem algebraischen Funktionenkörper mit vollkommenem Konstantenkörper bei beliebiger Charakteristik, J. Reine Angew. Math, vol.175, pp.50-54, 1936.
, Asymptotically fast solution of Toeplitz-like singular linear systems, Proceedings of the international symposium on Symbolic and algebraic computation , ISSAC '94, pp.297-304, 1994.
DOI : 10.1145/190347.190431
, On wiedemann's method of solving sparse linear systems, AAECC-9, pp.29-38, 1991.
DOI : 10.1007/3-540-54522-0_93
, The Re-Encoding Transformation in Algebraic List-Decoding of Reed–Solomon Codes, IEEE Transactions on Information Theory, vol.57, issue.2, pp.633-647, 2011.
DOI : 10.1109/TIT.2010.2096034
, Algebraic soft-decision decoding of reed-solomon codes, IEEE Transactions on Information Theory, vol.49, issue.11, pp.2809-2825, 2003.
DOI : 10.1109/TIT.2003.819332
, A complexity reducing transformation in algebraic list decoding of Reed-Solomon codes, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674), pp.10-13, 2003.
DOI : 10.1109/ITW.2003.1216682
, Fast generalized minimum-distance decoding of algebraic-geometry and Reed-Solomon codes, IEEE Transactions on Information Theory, vol.42, issue.3, pp.721-737, 1996.
DOI : 10.1109/18.490540
, Powers of tensors and fast matrix multiplication, Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, ISSAC '14, pp.296-303, 2014.
DOI : 10.1145/2608628.2608664
, List decoding of Reed???Solomon codes from a Gr??bner basis perspective, Journal of Symbolic Computation, vol.43, issue.9, pp.645-658, 2008.
DOI : 10.1016/j.jsc.2008.01.002
, The Guruswami-Sudan decoding algorithm for Reed-Solomon codes, IPN Progress Report, pp.42-153, 2003.
, The construction of multivariate polynomials with preassigned zeros, EUROCAM'82, pp.24-31, 1982.
DOI : 10.1007/3-540-11607-9_3
, Doubling algorithms for Toeplitz and related equations, ICASSP '80. IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.954-959, 1980.
DOI : 10.1109/ICASSP.1980.1171074
, List Decoding of Algebraic Codes, 2013.
, Decoding Reed-Solomon Codes Beyond Half the Minimum Distance, Coding Theory, Cryptography and Related Areas, pp.221-236, 2000.
DOI : 10.1007/978-3-642-57189-3_20
, A displacement approach to efficient decoding of algebraic-geometric codes, Proceedings of the thirty-first annual ACM symposium on Theory of computing , STOC '99, pp.235-244, 1999.
DOI : 10.1145/301250.301311
, Correcting Errors Beyond the Guruswami-Sudan Radius in Polynomial Time, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05), pp.285-294, 2005.
DOI : 10.1109/SFCS.2005.29
, Algorithme LLL polynomial et applications Master's thesis, ´ Ecole Polytechnique Available at https, 2003.
, Introduction to Coding Theory, 2007.
DOI : 10.1017/CBO9780511808968
, Efficient decoding of Reed-Solomon codes beyond half the minimum distance, IEEE Transactions on Information Theory, vol.46, issue.1, pp.246-257, 2000.
DOI : 10.1109/18.817522
, Normalization of row reduced matrices, Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '11, pp.297-304, 2011.
DOI : 10.1145/1993886.1993931
, Fast Probabilistic Algorithms for Verification of Polynomial Identities, Journal of the ACM, vol.27, issue.4, pp.701-717, 1980.
DOI : 10.1145/322217.322225
, A fast deterministic algorithm for factoring polynomials over finite fields of small characteristic, Proceedings of the 1991 international symposium on Symbolic and algebraic computation , ISSAC '91, pp.14-21, 1991.
DOI : 10.1145/120694.120697
, Notes on computing minimal approximant bases, Challenges in Symbolic Computation Software, Dagstuhl Seminar Proceedings, 2006.
, On the Complexity of Matrix Multiplication, 2010.
, Decoding of Reed Solomon Codes beyond the Error-Correction Bound, Journal of Complexity, vol.13, issue.1, pp.180-193, 1997.
DOI : 10.1006/jcom.1997.0439
, Efficient Interpolation in the Guruswami–Sudan Algorithm, IEEE Transactions on Information Theory, vol.56, issue.9, pp.4341-4349, 2010.
DOI : 10.1109/TIT.2010.2053901
, Multiplying matrices faster than coppersmith-winograd, Proceedings of the 44th symposium on Theory of Computing, STOC '12, pp.887-898, 2012.
DOI : 10.1145/2213977.2214056
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.2680
, New List Decoding Algorithms for Reed–Solomon and BCH Codes, IEEE Transactions on Information Theory, vol.54, issue.8, pp.3611-3630, 2008.
DOI : 10.1109/TIT.2008.926355
, Algebraic Soft-and Hard-Decision Decoding of Generalized Reed?Solomon and Cyclic Codes, 2013.
URL : https://hal.archives-ouvertes.fr/pastel-00866134
, An Interpolation Procedure for List Decoding Reed–Solomon Codes Based on Generalized Key Equations, IEEE Transactions on Information Theory, vol.57, issue.9, pp.5946-5959, 2011.
DOI : 10.1109/TIT.2011.2162160