K. Lee and M. E. O-'sullivan, List decoding of Hermitian codes using Gr??bner bases, Journal of Symbolic Computation, vol.44, issue.12, pp.1662-1675, 2009.
DOI : 10.1016/j.jsc.2007.12.004

P. Beelen and K. Brander, Efficient list decoding of a class of algebraic-geometry codes, Adv. Mathematics of Comm, vol.4, pp.485-518, 2010.

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

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

J. S. Nielsen, Power Decoding of Reed???Solomon Codes Revisited, ICMCTA, 2014.
DOI : 10.1007/978-3-319-17296-5_32

S. Sakata, H. E. Jensen, and T. Høholdt, Generalized Berlekamp-Massey decoding of algebraic-geometric codes up to half the Feng-Rao bound, IEEE Transactions on Information Theory, vol.41, issue.6, pp.1762-1768, 1995.
DOI : 10.1109/18.476248

H. Stichtenoth, A note on Hermitian codes over GF(q/sup 2/), IEEE Transactions on Information Theory, vol.34, issue.5, pp.1345-1348, 1988.
DOI : 10.1109/18.21267

K. Brander, Interpolation and List Decoding of Algebraic Codes, 2010.

H. Stichtenoth, Algebraic Function Fields and Codes, 2009.

K. Yang and P. V. Kumar, On the true minimum distance of Hermitian codes, Coding Theory and Algebraic Geometry, pp.99-107, 1992.
DOI : 10.1007/BFb0087995

J. S. Nielsen, Solving generalised Padé approximations over polynomial rings, Preprint, 2014.

J. S. Nielsen, List Decoding of Algebraic Codes, 2013.

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

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

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

J. S. Nielsen, Generalised Multi-sequence Shift-Register synthesis using module minimisation, 2013 IEEE International Symposium on Information Theory, 2013.
DOI : 10.1109/ISIT.2013.6620353

V. Guruswami and M. Sudan, Improved decoding of Reed-Solomon and algebraic-geometric codes, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280), pp.1757-1767, 1999.
DOI : 10.1109/SFCS.1998.743426

P. Beelen and T. Høholdt, The Decoding of Algebraic Geometry Codes, Advances in Algebraic Geometry Codes (E. Martínez-Moro, 2008.
DOI : 10.1142/9789812794017_0002

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, 1284.
DOI : 10.3934/amc.2015.9.311

X. Wu and P. H. Siegel, Efficient root-finding algorithm with application to list decoding of algebraic-geometric codes, IEEE Trans. Inf. Theory, vol.47, issue.6, pp.2579-2587, 2001.

R. Roth and G. Ruckenstein, 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

J. Justesen, K. J. Larsen, H. E. Jensen, and T. Høholdt, Fast decoding of codes from algebraic plane curves, IEEE Transactions on Information Theory, vol.38, issue.1, pp.111-119, 1992.
DOI : 10.1109/18.108255

G. Schmidt, V. Sidorenko, and M. Bossert, Syndrome Decoding of Reed–Solomon Codes Beyond Half the Minimum Distance Based on Shift-Register Synthesis, IEEE Transactions on Information Theory, vol.56, issue.10, pp.5245-5252, 2010.
DOI : 10.1109/TIT.2010.2060130

S. Kampf, Bounds on collaborative decoding of interleaved Hermitian codes and virtual extension, Designs, Codes and Cryptography, pp.1-17, 2012.
DOI : 10.1007/s10623-012-9625-2

S. Kampf and W. Li, Decoding interleaved Reed?Solomon and Hermitian codes with generalized divisions, Proc. of SCC, pp.1-6, 2013.

A. Zeh, A. Wachter, and M. Bossert, Unambiguous decoding of generalized Reed?Solomon codes beyond half the minimum distance, Proc. of IZS, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01120389

H. E. Jensen, R. R. Nielsen, and T. Høholdt, Performance analysis of a decoding algorithm for algebraic-geometry codes, IEEE Transactions on Information Theory, vol.45, issue.5, pp.1712-1717, 1999.
DOI : 10.1109/18.771253

J. P. Hansen, Dependent rational points on curves over finite fields - Lefschetz theorems and exponential sums, Proc. of WCC, pp.297-309, 2001.
DOI : 10.1016/S1571-0653(04)00181-7

G. Feng, V. K. Wei, T. R. Rao, and K. K. Tzeng, Simplified understanding and efficient decoding of a class of algebraic-geometric codes, IEEE Transactions on Information Theory, vol.40, issue.4, pp.981-1002, 1994.
DOI : 10.1109/18.335973

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

S. Sakata, J. Justesen, Y. Madelung, H. E. Jensen, and T. Høholdt, A Fast Decoding Method of AG Codes from Miura-Kamiya Curves Cab up to Half the Feng-Rao Bound, Finite Fields and Their Applications, vol.1, issue.1, pp.83-101, 1995.
DOI : 10.1006/ffta.1995.1006

A. Aho, J. Hopcroft, and J. Ullman, The Design and Analysis Of Computer Algorithms, 1974.

J. Zur-gathen and J. Gerhard, Modern Computer Algebra, 2012.
DOI : 10.1017/CBO9781139856065

T. H. Cormen, C. E. Leierson, R. L. Rivest, and C. Stein, Introduction to algorithms, 2009.