M. Alekhnovich, Linear Diophantine equations over polynomials and soft decoding of Reed-Solomon codes, FOCS'02, pp.439-448, 2002.

M. Alekhnovich, 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

B. Beckermann, 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

B. Beckermann and G. Labahn, 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

B. Beckermann and G. Labahn, Fraction-Free Computation of Matrix Rational Interpolants and Matrix GCDs, SIAM Journal on Matrix Analysis and Applications, vol.22, issue.1, pp.114-144, 2000.
DOI : 10.1137/S0895479897326912

B. Beckermann, G. Labahn, and G. Villard, Normal forms for general polynomial matrices, Journal of Symbolic Computation, vol.41, issue.6, pp.708-737, 2006.
DOI : 10.1016/j.jsc.2006.02.001

P. Busse, Multivariate List Decoding of Evaluation Codes with a Gröbner Basis Perspective, 2008.

M. Chowdhury, C. Jeannerod, V. Neiger, ´. E. Schost, and G. Villard, Faster Algorithms for Multivariate Interpolation With Multiplicities and Simultaneous Polynomial Approximations, IEEE Transactions on Information Theory, vol.61, issue.5, pp.612370-2387, 2015.
DOI : 10.1109/TIT.2015.2416068

URL : https://hal.archives-ouvertes.fr/hal-00941435

H. Cohn and N. Heninger, Approximate common divisors via lattices, Tenth Algorithmic Number Theory Symposium, pp.271-293
DOI : 10.2140/obs.2013.1.271

H. Cohn and N. Heninger, Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding, Advances in Mathematics of Communications, vol.9, issue.3, pp.311-339, 2015.
DOI : 10.3934/amc.2015.9.311

D. Coppersmith and S. Winograd, 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

C. Devet, I. Goldberg, and N. Heninger, Optimally robust private information retrieval, Cryptology ePrint Archive, 2012.

J. Zur-gathen and J. Gerhard, Modern Computer Algebra (third edition), 2013.

P. Giorgi, C. Jeannerod, and G. Villard, 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

S. Gupta, Hermite forms of polynomial matrices, 2011.

S. Gupta, S. Sarkar, A. Storjohann, and J. Valeriote, 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

S. Gupta and A. Storjohann, Computing hermite forms of polynomial matrices, Proceedings of the 36th international symposium on Symbolic and algebraic computation, ISSAC '11, pp.155-162, 2011.
DOI : 10.1145/1993886.1993913

J. L. Hafner and K. Mccurley, Asymptotically Fast Triangularization of Matrices over Rings, SIAM Journal on Computing, vol.20, issue.6, pp.1068-1083, 1991.
DOI : 10.1137/0220067

C. Hermite, Sur l'introduction des variables continues dans la théorie des nombres, Journal für die reine und angewandte Mathematik, pp.191-216, 1851.

C. Jeannerod, V. Neiger, ´. E. Schost, and G. Villard, Computing minimal interpolation bases. HAL Open archive -https, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01241781

C. Jeannerod, V. Neiger, ´. E. Schost, and G. Villard, Fast computation of minimal interpolation bases in Popov form for arbitrary shifts. HAL Open archive -https, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01265983

T. Kailath, Linear Systems, 1980.

E. Kaltofen, M. S. Krishnamoorthy, and D. Saunders, Parallel algorithms for matrix normal forms, Linear Algebra and its Applications, vol.136, pp.189-208, 1990.
DOI : 10.1016/0024-3795(90)90028-B

S. Lang, Algebra (Revised Third Edition), 2002.

F. and L. Gall, 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

T. Mulders and A. Storjohann, On lattice reduction for polynomial matrices, Journal of Symbolic Computation, vol.35, issue.4, pp.377-401, 2003.
DOI : 10.1016/S0747-7171(02)00139-6

V. M. Popov, Invariant Description of Linear, Time-Invariant Controllable Systems, SIAM Journal on Control, vol.10, issue.2, pp.252-264, 1972.
DOI : 10.1137/0310020

S. Sarkar and A. Storjohann, 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

A. Storjohann, High-order lifting and integrality certification, Journal of Symbolic Computation, vol.36, issue.3-4, pp.613-648, 2003.
DOI : 10.1016/S0747-7171(03)00097-X

A. Storjohann, Notes on computing minimal approximant bases, Dagstuhl Seminar Proceedings, 2006.

A. Storjohann and G. Labahn, Asymptotically fast computation of Hermite normal forms of integer matrices, Proceedings of the 1996 international symposium on Symbolic and algebraic computation , ISSAC '96, pp.259-266, 1996.
DOI : 10.1145/236869.237083

M. , V. Barel, and A. Bultheel, A general module theoretic framework for vector M-Padé and matrix rational interpolation, Numer. Algorithms, vol.3, pp.451-462, 1992.

G. Villard, Computing Popov and Hermite forms of polynomial matrices, Proceedings of the 1996 international symposium on Symbolic and algebraic computation , ISSAC '96, pp.250-258, 1996.
DOI : 10.1145/236869.237082

W. Zhou and G. Labahn, Efficient algorithms for order basis computation, Journal of Symbolic Computation, vol.47, issue.7, pp.793-819, 2012.
DOI : 10.1016/j.jsc.2011.12.009

W. Zhou and G. Labahn, A fast, deterministic algorithm for computing a Hermite normal form of a polynomial matrix. arXiv e-Print archive http, 2016.

W. Zhou, G. Labahn, and A. Storjohann, Computing minimal nullspace bases, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pp.366-373, 2012.
DOI : 10.1145/2442829.2442881

W. Zhou, G. Labahn, and A. Storjohann, A deterministic algorithm for inverting a polynomial matrix, Journal of Complexity, vol.31, issue.2, pp.162-173, 2015.
DOI : 10.1016/j.jco.2014.09.004