B. Sugiyama, Augot and Levy-dit-Vehel [A-AL96], Boston [A-Bos01], Duursma and Pellikaan [A-DP06] as well as Beei and Sala [A-BS06]. An extensive discussion can be found in van Lint's book [B-Lin99, Chapter 6], in the preliminary version of Pellikaan et. al. [B-PWBJ12, Chapter 7], Charpin's chapter [O-Cha98] in the Handbook of Coding eory, Blahut's book [B-PHB98b, Chapter 19 e survey paper of Augot et al. [O-ACS91] also gives an overview on the existing bounds. Although these improved bounds show that for many codes the actual distance is higher than the BCH bound, there is no general decoding algorithm up the actual distance of cyclic codes. Hartmann and Tzeng [A-Har72; A-HT74] proposed two variants of an iterative decoding algorithm up to their bound. However, these algorithms require the calculation of missing syndromes and the solution of non-linear equations. An approach for decoding all binary cyclic codes up to their actual minimum distance of length less than 63 was given by Feng and Tzeng, quadratic-time up to the Hartmann?Tzeng bound. Further Peterson and Weldon [B-PW72, Chapter 8] and in the book of MacWilliams and Sloane [B-MS88a, ChapterTF94]. ey use a generalized syndrome matrix and t the known syndrome coeecients manually for each code into the structure of the matrix. Various other decoding variants exist. is chapter covers parts of the published work [I-ZWB11; I-ZB12c; A-ZWB12b; A-ZB12a

M. Aaa and M. K. , A Parametric Approach to List Decoding of Reed?Solomon Codes Using Interpolation, IEEE Trans. Inform. eory, vol.5710, pp.6718-6728, 2011.

D. and F. Llllvvvvv, Bounds on the Minimum Distance of the Duals of BCH Codes, IEEE Trans. Inform. eory, vol.42, issue.4, 1996.

M. Aaaaaaa, Linear Diophantine Equations over Polynomials and Soo Decoding of Reed?Solomon Codes, IEEE Trans. Inform. eory, vol.517, pp.2257-2265, 2005.

M. A. Aaaaaa, A Note on Interleaved Reed-Solomon Codes Over Galois Rings, IEEE Trans. Inform. eory, vol.56, issue.4, pp.1574-1581, 2010.

L. A. Bbbbbb, New Upper Bounds for Error-Correcting Codes, Probl. Inf. Transm, vol.1, issue.16, pp.41-44, 1965.

P. Bbbbbb and K. Bbbbbbb, EEcient List Decoding of a Class of Algebraic-Geometry Codes, Adv. Math. Commun, vol.44, pp.485-518, 2010.

P. Bbbbbb and K. Bbbbbbb, Key Equations for List Decoding of Reed?Solomon Codes and How to Solve em, J. Symbolic Comput, vol.457, pp.773-786, 2010.

E. R. Bbbbbbbbb, A Survey of Coding eory, Stat. Soc. Ser. A, vol.1351, pp.44-73, 1972.

M. Bbb, J. Hhhhhh, and S. Hhhhhhh, Partial-MDS Codes and their Application to RAID Type of Architectures, IEEE Trans. Inform. eory, 2013.

[. Bbbbb, C. Hhhhhhh, T. Hhhhhh, and V. Www, Algebraic-Geometry Codes, IEEE Trans. Inform. eory, vol.446, 1998.

[. Bbbbbb, T. Hhhhhh, J. S. Nnnnnnn, and Y. W. , On Rational Interpolation-Based List-Decoding and List-Decoding Binary Goppa Codes, IEEE Trans. Inform. eory, vol.596, pp.3269-3281, 2013.

E. R. Bbbbbbbbb and J. Jjjjjjjj, Some Long Cyclic Linear Binary Codes Are Not So Bad, IEEE Trans. Inform. eory, vol.203, pp.351-356, 1974.

J. Bbbbbbbbb and A. Kk, Low-Complexity Soo-Decoding Algorithms for Reed? Solomon Codes?Part I: An Algebraic Soo-In Hard-Out Chase Decoder

J. Bbbbbbbbb, A. Kk, M. Mmmmm, and L. Pppp, Low-Complexity Soo-Decoding Algorithms for Reed-Solomon Codes?Part II: Soo-Input Soo-Output Iterative Decoding

D. Bbbbbbbbbb, A. Kkk, and M. Y. , Decoding Interleaved Reed?Solomon Codes over Noisy Channels " . eor, Comput. Sci, vol.3793, pp.348-360, 2007.

[. R. Bbbbbbbbb, R. Mmeeeeee, and H. C. Ttttttt, On the Inherent Intractability of Certain Coding Problems, IEEE Trans. Inform. eory, vol.243, pp.384-386, 1978.

[. Bbbb, Bounding Minimum Distances of Cyclic Codes Using Algebraic Geometry

R. C. Bbbb and D. K. Rrccc, On A Class of Error Correcting Binary Group Codes, Inf. Control, vol.3160, issue.107, pp.68-79, 1960.

E. Bbbbb and M. Ssss, A New Bound for the Minimum Distance of a Cyclic Code From Its Deening Set, IEEE Trans. Inform. eory, vol.528, pp.3700-3706, 2006.

H. Bbbb and E. Wwwwww, Cyclic Product Codes, IEEE Trans. Inform. eory, vol.113, pp.433-439, 1965.

E. L. Bbbbb and V. V. Zz, Coding of Generalized Concatenated Codes

D. J. Cccccccc and G. D. Ffffff, Channel Coding: e Road to Channel Capacity

D. Ccccc, Class of Algorithms for Decoding Block Codes With Channel Measurement Information, IEEE Trans. Inform. eory, vol.181, pp.170-182, 1972.

R. Ccccc, Cyclic Decoding Procedures for Bose-Chaudhuri-Hocquenghem Codes

P. Ccccccc, A. Tttt¨¨tttt¨¨, and V. A. Zzzz, On Binary Cyclic Codes with Minimum Distance d = 3, Probl. Inf. Transm, vol.334, issue.17, pp.287-296, 1997.

P. Ccccccc, A. Tttt¨¨tttt¨¨, and V. A. Zzzz, On the Minimum Distances of Non-Binary Cyclic Codes, Des. Codes Cryptogr, vol.17, issue.134, pp.81-851008354504832, 1999.

D. Dddddd and I. F. Bbbbb, Fast Parallel Algorithms for Decoding Reed?Solomon Codes Based on Remainder Polynomials, IEEE Trans. Inform. eory, vol.41, issue.4, pp.873-885, 1995.

P. Dddddddd, On Subbeld Subcodes of Modiied Reed?Solomon Codes, IEEE Trans

P. Dddddddd, Bilinear Forms over a Finite Field, with Applications to Coding eory

I. M. Ddddddd, R. K¨, and . K¨, Error-Locating Pairs for Cyclic Codes, IEEE Trans

I. I. Ddddd, G. A. Kkkk, and C. T. , List Decoding of the First-Order Binary Reed?Muller Codes, Probl. Inf. Transm, vol.433, pp.225-232, 2007.

I. I. Ddddd, D. Mmmmmmmmmm, and M. Sss, Hardness of Approximating the Minimum Distance of a Linear Code, IEEE Trans. Inform. eory, vol.491, pp.22-37, 2003.

J. Ddddddddddd, On the Equivalence Between Berlekamp's and Euclid's Algorithms

I. M. Ddddddd and R. Ppppppppp, A Symmetric Roos Bound for Linear Codes Journal of Combinatorial eory Series A -Special Issue in Honor of, J. H. van Lint, vol.113, pp.1677-1688, 2006.

M. E. Eeekkkkk and R. J. Mmmmmmmm, Iterative Algebraic Soo-Decision List Decoding of Reed?Solomon Codes, IEEE J. Sel. Areas Commun, vol.243, pp.481-490, 2006.

P. Eeeee, Error-Free Coding, IEEE Trans. Inform. eory, vol.44, pp.29-37, 1954.

G. D. Ffffff, On Decoding BCH Codes, IEEE Trans. Inform. eory, vol.11, issue.120, pp.549-557, 1965.

G. D. Ffffff, Generalized Minimum Distance Decoding, IEEE Trans. Inform. eory, vol.122, pp.125-131, 1966.

R. Fffffff and C. T. , An Improved List Decoding Algorithm for the Second Order Reed?Muller Codes and its Applications, Des. Codes Cryptogr, vol.49, pp.323-340, 2008.

G. L. Ffff and K. Ttttt, An Iterative Algorithm of Shii-Register Synthesis for Multiple Sequences, Scientia Sinica (Series A), vol.2811, pp.1222-1232, 1985.

G. L. Ffff and K. Ttttt, A Generalized Euclidean Algorithm for Multisequence Shii-Register Synthesis, IEEE Trans. Inform. eory, vol.353, issue.107, pp.584-594, 1989.

G. L. Ffff and K. Ttttt, A Generalization of the Berlekamp?Massey Algorithm for Multisequence Shii-Register Synthesis with Applications to Decoding Cyclic Codes

G. L. Ffff and K. Ttttt, Decoding Cyclic and BCH Codes up to Actual Minimum Distance Using Nonrecurrent Syndrome Dependence Relations, IEEE Trans. Inform. eory, vol.376, issue.53, pp.1716-1723, 1991.

E. M. Ggggggggg, eory of Codes with Maximum Rank Distance, Probl. Peredachi Inf, vol.211, pp.3-16, 1985.

W. Ggggg, F. Kkkkkkkkkkk, R. K¨, K. , and P. Ggggg, Applications of Algebraic Soo- Decision Decoding of Reed?Solomon Codes, IEEE Trans. Commun, vol.547, 2006.

V. D. Gggg, A New Class of Linear Error Correcting Codes, Probl. Peredachi. Inf, vol.6, pp.24-30, 1970.

V. D. Gggg, Rational Representation of Codes and (L,g) Codes, Probl. Peredachi. Inf, vol.7, pp.41-49, 1971.

W. Gggg, Further Results on Product Codes, IEEE Trans. Inform. eory, vol.164, pp.446-451, 1970.

V. Gggggg and A. Rrrrr, Explicit Codes Achieving List Decoding Capacity: Error- Correction With Optimal Redundancy, IEEE Trans. Inform. eory, vol.541, pp.135-150, 2008.

O. Ggggggggg, D. Rrr, and M. Sss, Chinese Remaindering with Errors, IEEE Trans

O. Ggggggggg, R. Rrrrrrrrr, and M. Sss, Learning Polynomials with eries: e Highly Noisy Case, SIAM J. Discrete Math, vol.134, pp.535-570, 2000.

P. Ggggggg and M. Sss, Highly Resilient Correctors for Polynomials, Inform

V. Gggggg and M. Sss, Improved Decoding of Reed?Solomon and Algebraic- Geometry Codes, IEEE Trans. Inform. eory, vol.456, issue.65, pp.1757-1767, 1999.

V. Gggggg and A. V. , Maximum-Likelihood Decoding of Reed?Solomon Codes is NP-Hard, IEEE Trans. Inform. eory, vol.517, pp.2249-2256, 2005.

V. Gggggg and C. W. , Linear-Algebraic List Decoding for Variants of Reed?Solomon Codes, Electronic Colloquium on Computational Complexity (ECCC), vol.1973, pp.1-24, 2012.

D. Gggggggggg and N. Zzzzzzz, A Class of Error-Correcting Codes in p m, J. Soc. Ind

R. W. Hhhhhhh, Error Detecting and Error Correcting Codes, Bell Syst. Tech. J, vol.29, issue.2, pp.147-160, 1950.

C. Hhhhhhhh, Decoding Beyond the BCH Bound, IEEE Trans. Inform. eory, vol.183, issue.107, pp.441-444, 1972.

H. Hhhhh, eorie der höheren Diierentiale in einem algebraischen Funktionenkörper mit vollkommenem Konstantenkörper bei beliebiger Charakteristik, J. Reine Angew. Math, vol.1936175, pp.50-54, 1936.

C. Hhhhhhh, Sur la Formule d'Interpolation de Lagrange, J. Reine Angew. Math, vol.841, pp.70-79, 1878.

A. Hhhhhhhhhh, Codes Correcteurs d'Erreurs, Chiires (Paris), pp.147-156, 1959.

C. Hhhhhhhh and K. Ttttt, Generalizations of the BCH Bound, Inf. Control, vol.205, issue.107, pp.489-498, 1972.

C. Hhhhhhhh and K. Ttttt, Decoding Beyond the BCH Bound Using Multiple Sets of Syndrome Sequences, IEEE Trans. Inform. eory, vol.20, issue.107, pp.292-295, 1974.

C. Hhhhhhhh, K. Ttttt, and R. Ccccc, Some Results on the Minimum Distance Structure of Cyclic Codes, IEEE Trans. Inform. eory, vol.183, issue.107, pp.402-409, 1972.

J. Jjjjjj, e Concatenated Structure of Cyclic and Abelian Codes, IEEE Trans. Inform. eory, vol.316, pp.788-793, 1985.

J. Jjjjjj, Cyclic Concatenated Codes with Constacyclic Outer Codes, IEEE Trans

J. Jjjjjj and A. Hhhh, On the Equivalence of the Berlekamp?Massey and the Euclidean Algorithms for Decoding, IEEE Trans. Inform. eory, vol.467, pp.2614-2624, 2000.

J. Jjjjj and K. Nnnn, Iterative Soo Decoding of Reed?Solomon Codes, IEEE Commun. Lee, vol.84, pp.244-246, 2004.

J. Jjjjj and K. Nnnn, Iterative Soo-Input Soo-Output Decoding of Reed? Solomon Codes by Adapting the Parity-Check Matrix, IEEE Trans. Inform. eory, vol.528, pp.3746-3756, 2006.

[. Jjjjjjj, A New Upper Bound for Error-Correcting Codes, IRE Trans. Inf. eor, vol.83, pp.203-207, 1962.

R. K. K¨, Fast Generalized Minimum-Distance Decoding of Algebraic-Geometry and Reed?Solomon Codes, IEEE Trans. Inform. eory, vol.423, issue.101, pp.721-737, 1996.

R. Känd and F. Kkkkkkkkkkk, Coding for Errors and Erasures in Random Network Coding, IEEE Trans. Inform. eory, vol.548, pp.3579-3591, 2008.

R. K¨, K. , J. Mm, and A. V. , e Re-Encoding Transformation in Algebraic List- Decoding of Reed?Solomon Codes, IEEE Trans. Inform. eory, vol.57, issue.101 102, pp.633-647, 2011.

V. Kkk, Reed?Solomon Codes for Correcting Phased Error Bursts, IEEE Trans. Inform. eory, vol.4911, pp.2975-2984, 2003.

V. Kkk, Decoding for Iterative Reed?Solomon Coding Schemes, IEEE Trans

R. Känd and A. V. , Algebraic Soo-Decision Decoding of Reed?Solomon Codes

K. Lll and M. E. O-'ssssss, List Decoding of Hermitian Codes using Gröbner Bases

[. Lll and E. J. Wwwwww, Further Results on Cyclic Product Codes, IEEE Trans. Inform. eory, vol.16, issue.30, pp.452-459, 1970.

J. Llll and R. W. , On e Minimum Distance of Cyclic Codes, IEEE Trans

D. Mmmmmmmm, On a Class of Arithmetic Codes and a Decoding Algorithm, IEEE Trans. Inform. eory, vol.221, pp.85-88, 1976.

A. Mmmmmmm, Summation of the Products of Codes, Probl. Inf. Transm, vol.4, issue.2, pp.8-15, 1968.

J. L. Mmmmmm, Reversible Codes, Inf. Control, vol.7364, issue.112, pp.369-38090438, 1964.

J. L. Mmmmmm, Shii-Register Synthesis and BCH Decoding, IEEE Trans. Inform. eory, vol.151, issue.107, pp.122-127, 1969.

D. Mmmmmm, Application of Boolean Algebra to Switching Circuit Design and to Error Detection, IRE Trans. Inf. eor, vol.33, pp.6-12, 1954.

W. Pppppppp, Encoding and Error-Correction Procedures for the Bose- Chaudhuri Codes, IEEE Trans. Inform. eory, vol.64, pp.459-470, 1960.

J. S. Ppppp, A Tutorial on Reed?Solomon Coding for Fault-Tolerance in RAID-Like Systems, 9¡995::AID-SPE111¿3.3.CO, pp.995-10122, 1997.

I. Rrrr, A Class of Multiple-Error-Correcting Codes and the Decoding Scheme, IEEE Trans. Inform. eory, vol.4, issue.4, pp.38-49, 1954.

P. Rrrrr and J. Llll, More on the Minimum Distance of Cyclic Codes, IEEE Trans. Inform. eory, vol.371, pp.187-189, 1991.

C. Rrrr, A Generalization of the BCH Bound for Cyclic Codes, Including the Hartmann? Tzeng Bound, J. Combin. eory Ser. A, vol.3382, issue.2, pp.229-232, 1982.

C. Rrrr, A New Lower Bound for the Minimum Distance of a Cyclic Code, IEEE Trans

R. Rr, Maximum-Rank Array Codes and eir Application to Crisscross Error Correction, IEEE Trans. Inform. eory, vol.37, issue.2, pp.328-336, 1991.

R. Rr and G. Rrrrrrrrrrr, EEcient Decoding of Reed?Solomon Codes Beyond Half the Minimum Distance, IEEE Trans. Inform. eory, vol.461, pp.246-257, 2000.

I. S. Rrrr and G. Sssssss, Polynomial Codes Over Certain Finite Fields, J. Soc. Ind

C. E. Sssssss, A Mathematical eory of Communication, Bell Syst. Tech. J, vol.27, pp.370-423, 1948.

A. Sssssssssss, Raptor Codes, IEEE Trans. Inform. eory, vol.526, pp.2551-2567, 2006.

Y. Sssss, M. Kkkkkkkk, S. Hhhhhh, and T. Nnnnnn, A Method for Solving Key Equation for Decoding Goppa Codes, Inf. Control, vol.27175, issue.107, pp.87-99, 1975.

Y. Sssss, M. Kkkkkkkk, S. Hhhhhh, and T. Nnnnnn, An Erasures-and-Errors Decoding Algorithm for Goppa Codes, IEEE Trans. Inform. eory, vol.22, issue.107, pp.238-241, 1976.

D. Sss, F. Kkkkkkkkkkk, R. K¨, and . K¨, A Rank-Metric Approach to Error Control in Random Network Coding, IEEE Trans. Inform. eory, vol.54, issue.9, pp.3951-3967, 2008.

D. Sssssss, Some Further eory of Group Codes, Bell Syst. Tech. J, vol.395, issue.28, pp.1219-1252, 1960.

T. Sssss, C. Ll, and M. Xxx, Progressive List-Enlarged Algebraic Soo Decoding of Reed?Solomon Codes, IEEE Commun. Lee, vol.166, pp.901-904, 2012.

[. A. Ssssssss and E. T. Mmmmmmmmm, Cyclic (L,G) Codes, Probl. Peredachi. Inf, vol.172, pp.3-10, 1981.

A. Sssssssss, A Generalization of Hermite's Interpolation Formula

V. R. Ssssssss and G. Ssssss, A Linear Algebraic Approach to Multisequence Shii-Register Synthesis, Probl. Inf. Transm, vol.47, issue.131, pp.149-165, 2011.

G. Ssssss, V. R. Ssssssss, and M. Bbbbbbb, Collaborative Decoding of Interleaved Reed?Solomon Codes and Concatenated Code Designs, IEEE Trans. Inform. eory, vol.557, pp.2991-3012, 2009.

G. Ssssss, V. R. Ssssssss, and M. Bbbbbbb, Syndrome Decoding of Reed?Solomon Codes Beyond Half the Minimum Distance Based on Shii-Register Synthesis, IEEE Trans. Inform. eory, vol.5610, issue.68, pp.5245-5252, 2010.

M. Sss, Decoding of Reed?Solomon Codes Beyond the Error-Correction Bound, J

M. Sssssssssss and H. W. , List Decoding of Algebraic-Geometric Codes

K. Ssss, C. W. , K. Ttttt, and B. Z. Ssss, Generation of Matrices for Determining Minimum Distance and Decoding of Cyclic Codes, IEEE Trans. Inform. eory, vol.422, pp.653-657, 1996.

K. Ttttt and G. L. Ffff, A New Procedure for Decoding Cyclic and BCH Codes up to Actual Minimum Distance, IEEE Trans. Inform. eory, vol.405, pp.1364-1374, 1994.

P. Ttttttt, Interpolation in List Decoding of Reed?Solomon Codes

P. Ttttttt, EEcient Interpolation in the Guruswami?Sudan Algorithm, IEEE Trans

T. Y. and I. F. Bbbbb, Two New Decoding Algorithms for Reed?Solomon Codes, Appl. Algebra Engrg. Comm. Comput, vol.51, pp.23-43, 1994.

A. Zzz and S. Bbbbb, A New Bound on the Minimum Distance of Cyclic Codes Using Small-Minimum-Distance Cyclic Codes, Des. Codes Cryptogr, pp.1-18, 2012.

A. Zzz, C. Ggggggg, and D. A. , An Interpolation Procedure for List Decoding Reed?Solomon Codes Based on Generalized Key Equations, IEEE Trans. Inform. eory, vol.579, pp.5946-5959, 2011.

V. A. Zzzz, Generalized Cascade Codes, Probl. Inf. Transm, vol.121, issue.33, pp.5-15, 1976.

V. V. Zz, S. Sss, and M. Bbbbbbb, An Introduction to Generalized Concatenated Codes, Eur. Trans. Telecommun, vol.10, issue.34, pp.609-622, 1999.

A. Zzz and A. W. , Fast Multi-Sequence Shii-Register Synthesis with the Euclidean Algorithm, Adv. Math. Commun, vol.54, issue.131, pp.667-680, 2011.

[. Zzz, A. Wzzz, and S. V. Bbbbb, Decoding Cyclic Codes up to a New Bound on the Minimum Distance, IEEE Trans. Inform. eory, vol.586, issue.108, pp.3951-3960, 2012.

[. E. O-'ssssss, e Key Equation for One-Point Codes and EEcient Error Evaluation, J. Pure Appl. Algebra, vol.169, issue.01, pp.2-3, 2002.

A. Wzzz, Bounds on List Decoding of Rank Metric Codes, 2013.

E. R. Bbbbbbbbb, Algebraic Coding eory, 1968.

R. E. Bbbbbb, eory and Practice of Error Control Codes, 1983.

M. Bbbbbbb, Channel Coding for Telecommunications, 1999.

L. Cccc, List Decoding of Reed?Solomon Codes and Algebraic?Geometric Codes: Decoding Principles, Complexity Reduction and an Engineering Insight into the System, LAP Lambert Academic Publishing, 2009.

J. Gg and J. Ggggggg, Modern Computer Algebra, 2003.

V. Gggggg, List Decoding of Error-Correcting Codes, Lecture Notes in Computer Science, vol.3282, issue.64, p.62, 2004.

V. Gggggg, Algorithmic Results in List Decoding, 2007.

J. Jjjjjjjj and T. Hhhhhh, A Course in Error-Correcting Codes, p.43, 2004.

G. Kkkk, E. Kkkkk, and S. Ssssss, Error Correcting Coding and Security for Data Networks: Analysis of the Superchannel Concept, 2005.

[. Lll and D. J. Cccccccc, Error Control Coding, p.25, 2004.

J. Llll, Introduction to Coding eory, 1999.

J. D. Llllll, Elements of Algebra and Algebraic Computing, pp.50-51, 1981.

T. K. Mmmm, Error Correction Coding: Mathematical Methods and Algorithms, 2005.

F. Mmw and N. Sss, e eory of Error-Correcting Codes, pp.51-112, 1988.

V. S. Ppppp, W. C. Hhhhhhh, and R. A. Bbb, Handbook of Coding eory

W. W. Pppppppp and E. J. Wwwwww, Error-Correcting Codes, p.25, 1972.

R. Ppppppppp, X. W. , S. Bbb, and R. Jjjjjjj, Error-Correcting Codes and Cryptology (Preliminary Version, pp.2012-2037, 2012.

M. Aaaaaaa, Linear Diophantine Equations over Polynomials and Soo Decoding of Reed?Solomon Codes, IEEE Symposium on Foundations of Computer Science (FOCS). 2002, pp.439-448

D. and A. Zzz, On the Roth and Ruckenstein Equations for the Guruswami? Sudan Algorithm, IEEE International Symposium on Information eory (ISIT), pp.2620-2624, 2008.

[. Bbbbb and N. Ssssssss, One Generalization of Goppa Codes, IEEE International Symposium on Information eory (ISIT), 1997.

V. Gggggg, A. Sssss, and M. Sss, Soo-decision Decoding of Chinese Remainder Codes, IEEE Symposium on Foundations of Computer Science (FOCS). Redondo Beach, USA, pp.159-168, 2000.

T. Hhhhhh, P. Ed, J. By, J. Hhhhhhhhhh, and R. R. Ccc, List Decoding Using Syndromes Number eory and Its Applications, World Scientiic, vol.5, pp.315-331, 2008.

R. K. K¨, On Optimal Weight Assignmnents for Multivariate Interpolation List- Decoding, pp.37-41, 2006.

R. K¨, K. , J. Mm, A. V. , and A. Aaaaa, EEcient Interpolation and Factorization in Algebraic Soo-Decision Decoding of Reed?Solomon Codes, IEEE International Symposium on Information eory (ISIT). Yokohama, Japan, pp.365-365, 2003.

V. Kkk, Decoding of Parallel Reed?Solomon Codes with Applications to Product and Concatenated Codes, IEEE International Symposium on Information eory (ISIT), 1998.

R. Känd and A. V. , A Complexity Reducing Transformation in Algebraic List Decoding of Reed?Solomon Codes, pp.10-13, 2003.

K. Lll and M. O. Ssssss, An Interpolation Algorithm using Gröbner Bases for Soo-Decision Decoding of Reed-Solomon Codes, IEEE International Symposium on Information eory (ISIT). Seaale, USA, pp.2032-2036, 2006.

W. Ll and V. R. Ssssssss, On the Error-Erasure-Decoder of the Chinese Remainder Codes, International Symposium on Problems of Redundancy in Information and Control Systems (RED). 2012, pp.37-40

J. S. Nnnnnnn and A. Zzz, Multi-Trial Guruswami?Sudan Decoding for Generalised Reed?Solomon Codes, International Workshop on Coding and Cryptography (WCC). 2013 (cit, p.42

R. Rr and G. Rrrrrrrrrrr, EEcient Decoding of Reed?Solomon Codes Beyond Half the Minimum Distance, IEEE International Symposium on Information eory (ISIT)

G. Ssssss and V. R. Ssssssss, Multi-Sequence Linear Shii-Register Synthesis: e Varying Length Case, IEEE International Symposium on Information eory (ISIT), pp.1738-1742, 2006.

G. Ssssss, V. R. Ssssssss, and M. Bbbbbbb, Decoding Reed?Solomon Codes Beyond Half the Minimum Distance using Shii-Register Synthesis, IEEE International Symposium on Information eory (ISIT). Seaale, USA, pp.459-463, 2006.

M. Sss, Coding eory: Tutorial and Survey, IEEE Symposium on Foundations of Computer Science (FOCS, pp.36-51, 2001.

A. Zzz and S. Bbbbb, A New Error and Erasure Decoding Approach for Cyclic Codes, International Workshop on Algebraic and Combinatorial Coding eory (ACCT)

A. Zzz and S. Bbbbb, Describing a Cyclic Code by Another Cyclic Code, IEEE International Symposium on Information eory (ISIT), pp.2896-2900

A. Zzz, C. Ggggggg, and M. Bbbbbbb, EEcient List-Decoding of Reed?Solomon Codes with the Fundamental Iterative Algorithm, IEEE Information eory Workshop (ITW)

A. Zzz, A. W. , and S. Bbbbb, EEcient Decoding of Some Classes of Binary Cyclic Codes Beyond the Hartmann?Tzeng Bound, IEEE International Symposium on Information eory (ISIT). St, pp.1017-1021, 2011.

A. Zzz, A. W. , and M. Bbbb, Unambiguous Decoding of Generalized Reed? Solomon Codes Beyond Half the Minimum Distance " . International Zurich Seminar (IZS), pp.63-66

[. Zzz, A. Wzzz, M. Gggggggg, and S. Bbbbb, Generalizing Bounds on the Minimum Distance of Cyclic Codes Using Cyclic Product Codes, IEEE International Symposium on Information eory (ISIT), p.2013

R. J. Mmeeeeee, On the Average List Size for the Guruswami?Sudan Decoder, International Symposium on Communications eory and Applications (ISCTA). Ambleside, UK, 2003.

D. A. , P. Ccccccc, and N. Ssssssss, e Minimum Distance of Some Binary Codes via the Newton's Identities " . EUROCODE '90, Lecture Notes in Computer Science, vol.514, pp.65-73, 1991.

M. B. Aaaaándaaaa´aaaaánd and M. E. O-'ssssss, e Berlekamp?Massey Algorithm and the Euclidean Algorithm: a Closer Link, pp.1-12

M. Bbbbbbb, Décodage en liste et applicationàapplication`applicationà la sécurité de l'information, 2011.

[. Bbbbbbb, H. Gggggggg, J. Mm, and . Zz, Some Results on Generalized Concatenation of Block Codes Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Lecture Notes in Computer Science, vol.1719, pp.181-190, 1999.

P. Bbbbbb and T. Hhhhhh, A Syndrome Formulation of the Interpolation Step in the Guruswami?Sudan Algorithm " . Coding eory and Applications, Ed. by A. BBBBBBB. Lecture Notes in Computer Science, vol.5228, issue.67, pp.20-32, 2008.

P. Bbbbbb and T. Hhhhhh, e Decoding of Algebraic Geometry Codes, World Scientiic, vol.66, pp.49-98, 2008.

D. Bbbbbbbbbb, A. Kkk, M. Ed, J. C. By, J. K. Bbbbbb et al., Decoding of Interleaved Reed?Solomon Codes over Noisy Data, J. W. Lecture Notes in Computer Science, vol.2719, pp.97-108, 2003.

K. Bbbbbbb, Interpolation and List Decoding of Algebraic Codes, p.2010

P. , C. S. Ppppp, W. Hhhhhhh, and . Amsterdam, Open Problems on Cyclic Codes Handbook of Coding eory, pp.963-1064, 1998.

I. I. Ddddd, Concatenated Codes and eir Multilevel Generalizations Handbook of Coding eory, pp.1911-1988, 1998.

I. M. Ddddddd, Decoding Codes from Curves and Cyclic Codes, 1993.

P. Eeeee, List Decoding for Noisy Channels. Tech. rep. 335, 1957.

G. D. Ffffff, Concatenated Codes, Massachusees Institute of Technology (MIT), pp.16-31, 1966.

[. Gg, A New Algorithm for Decoding Reed?Solomon Codes " . Communications, Information and Network Security, International Series in Engineering and Computer Science, vol.712, pp.55-68, 2003.

H. Gggggggg, On Soo Concatenated Decoding of Block Codes, 2002.

J. I. Hhhh, Notes in Coding eory " . 2012 (cit, p.35

A. Hhhh, Decoding Algebraic Codes, 2001.

C. W. Hhhhhhh, W. Ppppp, . Hhhhhhh, and . Amsterdam, Codes and Groups Handbook of Coding eory, pp.1345-1440, 1998.

R. K. K¨, On Algebraic Decoding of Algebraic-Geometric and Cyclic Codes, 1996.

F. R. Kkkkkkkkkkk, Product Codes Wiley Encyclopedia of Telecommunications, p.29, 2003.

R. Känd and A. V. , Algebraic Soo-Decision of Reed-Solomon Codes, pp.62-97, 2000.

J. L. Mmmmmm and T. Ssss, Linear Complexity in Coding eory " . Coding eory and Applications, CCCCC and P. GGGGGGGGG. Lecture Notes in Computer Science, vol.311, pp.19-32, 1988.

J. S. Nnnnnnn, List Decoding of Algebraic Codes, p.2013

V. S. Ppppp, C. W. Hhhhhhh, and R. A. Bbb, An Introduction to Algebraic Codes

V. S. Ppppp, W. Hhhhhhh, and . Amsterdam, Handbook of Coding eory, pp.3-139, 1998.

E. Pppppp, Cyclic Error-Correcting Codes in Two Symbols. Tech. rep. Air Force Cambridge Research Center, p.16, 1957.

G. Rrrrrrrrrrr, Error Decoding Strategies for Algebraic Codes, pp.72-85, 2001.

G. Ssssss, Algebraic Decoding Beyond Half the Minimum Distance Based on Shii- Register Synthesis, p.67, 2007.

T. Ssss, A Linear Complexity Approach to Cyclic Codes Switzerland: Swiss Federal Institute of Technology in Zurich, 1988.

C. Ssssss, Generalized Minimum Distance Decoding with Arbitrary Error/Erasure Tradeoo, 2011.

M. S. Lllllll, O. W. , M. Hh, P. D. Mmmmmm, and T. Ii, List Decoding: Algorithms and Applications " . eoretical Computer Science: Exploring New Frontiers of eoretical Informatics, Lecture Notes in Computer Science, vol.1872, pp.25-41, 2000.

L. R. Wwwww and E. R. Bbbbbbbbb, Error Correction for Algebraic Block Codes, pp.16-40

R. J. Mmeeeeee, A Public-Key Cryptosystem Based on Algebraic Coding eory, pp.114-116, 1978.