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List decoding of matrix-product codes from nested codes: An application to quasi-cyclic codes
1. | Department of Mathematics, Universidad Jaume I, Campus Riu Sec, 12071, Castellón de la plana, Spain |
2. | DTU-Mathematics, Technical University of Denmark, Matematiktorvet, Building 303, 2800 Kgs. Lyngby, Denmark |
3. | Department of Mathematical Sciences, Aalborg University, Fr. Bajersvej 7G, 9920-Aalborg Øst, Denmark |
References:
[1] |
P. Beelen and K. Brander, Key equations for list decoding of Reed-Solomon codes and how to solve them, J. Symbolic Comput., 45 (2010), 773-786.
doi: 10.1016/j.jsc.2010.03.010. |
[2] |
T. Blackmore and G. H. Norton, Matrix-product codes over $\mathbb F_q$, Appl. Algebra Engrg. Comm. Comput., 12 (2001), 477-500.
doi: 10.1007/PL00004226. |
[3] |
I. I. Dumer, Concatenated codes and their multilevel generalizations, in "Handbook of Coding Theory,'' North-Holland, Amsterdam, (1998), 1911-1988. |
[4] |
P. Elias, List decoding for noisy channels, Rep. No. 335, Research Laboratory of Electronics, MIT, Cambridge, MA, 1957. |
[5] |
V. Guruswami and A. Rudra, Better binary list decodable codes via multilevel concatenation, IEEE Trans. Inform. Theory, 55 (2009), 19-26.
doi: 10.1109/TIT.2008.2008124. |
[6] |
V. Guruswami and M. Sudan, Improved decoding of Reed-Solomon and algebraic-geometry codes, IEEE Trans. Inform. Theory, 45 (1999), 1757-1767.
doi: 10.1109/18.782097. |
[7] |
F. Hernando, K. Lally and D. Ruano, Construction and decoding of matrix-product codes from nested codes, Appl. Algebra Engrg. Comm. Comput., 20 (2009), 497-507.
doi: 10.1007/s00200-009-0113-5. |
[8] |
F. Hernando and D. Ruano, New linear codes from matrix-product codes with polynomial units, Adv. Math. Commun., 4 (2010), 363-367.
doi: 10.3934/amc.2010.4.363. |
[9] |
T. Kasami, A Gilbert-Varshamov bound for quasi-cyclic codes of rate 1/2, IEEE Trans. Inform. Theory, IT-20 (1974), 679.
doi: 10.1109/TIT.1974.1055262. |
[10] |
K. Lally, Quasicyclic codes - some practical issues, in "Proceedings of 2002 IEEE International Symposium on Information Theory,'' 2002. |
[11] |
K. Lally and P. Fitzpatrick, Algebraic structure of quasicyclic codes, Discrete Appl. Math., 111 (2001), 157-175.
doi: 10.1016/S0166-218X(00)00350-4. |
[12] |
K. Lee and M. E. O'Sullivan, List decoding of Reed-Solomon codes from a Gröbner basis perspective, J. Symbolic Comput., 43 (2008), 645-658.
doi: 10.1016/j.jsc.2008.01.002. |
[13] |
R. R. Nielsen and T. Høholdt, Decoding Reed-Solomon codes beyond half the minimum distance, in "Coding Theory, Cryptography and Related Areas (Guanajuato, 1998),'' Springer, Berlin, (2000), 221-236. |
[14] |
F. Özbudak and H. Stichtenoth, Note on Niederreiter-Xing's propagation rule for linear codes, Appl. Algebra Engrg. Comm. Comput., 13 (2002), 53-56.
doi: 10.1007/s002000100091. |
[15] |
W. C. Schmid and R. Schürer, "Mint,'', Dept. of Mathematics, ().
|
[16] |
J. M. Wozencraft, List decoding, in "Quarterly Progress Report,'' MIT, Cambridge, MA, (1958), 90-95. |
show all references
References:
[1] |
P. Beelen and K. Brander, Key equations for list decoding of Reed-Solomon codes and how to solve them, J. Symbolic Comput., 45 (2010), 773-786.
doi: 10.1016/j.jsc.2010.03.010. |
[2] |
T. Blackmore and G. H. Norton, Matrix-product codes over $\mathbb F_q$, Appl. Algebra Engrg. Comm. Comput., 12 (2001), 477-500.
doi: 10.1007/PL00004226. |
[3] |
I. I. Dumer, Concatenated codes and their multilevel generalizations, in "Handbook of Coding Theory,'' North-Holland, Amsterdam, (1998), 1911-1988. |
[4] |
P. Elias, List decoding for noisy channels, Rep. No. 335, Research Laboratory of Electronics, MIT, Cambridge, MA, 1957. |
[5] |
V. Guruswami and A. Rudra, Better binary list decodable codes via multilevel concatenation, IEEE Trans. Inform. Theory, 55 (2009), 19-26.
doi: 10.1109/TIT.2008.2008124. |
[6] |
V. Guruswami and M. Sudan, Improved decoding of Reed-Solomon and algebraic-geometry codes, IEEE Trans. Inform. Theory, 45 (1999), 1757-1767.
doi: 10.1109/18.782097. |
[7] |
F. Hernando, K. Lally and D. Ruano, Construction and decoding of matrix-product codes from nested codes, Appl. Algebra Engrg. Comm. Comput., 20 (2009), 497-507.
doi: 10.1007/s00200-009-0113-5. |
[8] |
F. Hernando and D. Ruano, New linear codes from matrix-product codes with polynomial units, Adv. Math. Commun., 4 (2010), 363-367.
doi: 10.3934/amc.2010.4.363. |
[9] |
T. Kasami, A Gilbert-Varshamov bound for quasi-cyclic codes of rate 1/2, IEEE Trans. Inform. Theory, IT-20 (1974), 679.
doi: 10.1109/TIT.1974.1055262. |
[10] |
K. Lally, Quasicyclic codes - some practical issues, in "Proceedings of 2002 IEEE International Symposium on Information Theory,'' 2002. |
[11] |
K. Lally and P. Fitzpatrick, Algebraic structure of quasicyclic codes, Discrete Appl. Math., 111 (2001), 157-175.
doi: 10.1016/S0166-218X(00)00350-4. |
[12] |
K. Lee and M. E. O'Sullivan, List decoding of Reed-Solomon codes from a Gröbner basis perspective, J. Symbolic Comput., 43 (2008), 645-658.
doi: 10.1016/j.jsc.2008.01.002. |
[13] |
R. R. Nielsen and T. Høholdt, Decoding Reed-Solomon codes beyond half the minimum distance, in "Coding Theory, Cryptography and Related Areas (Guanajuato, 1998),'' Springer, Berlin, (2000), 221-236. |
[14] |
F. Özbudak and H. Stichtenoth, Note on Niederreiter-Xing's propagation rule for linear codes, Appl. Algebra Engrg. Comm. Comput., 13 (2002), 53-56.
doi: 10.1007/s002000100091. |
[15] |
W. C. Schmid and R. Schürer, "Mint,'', Dept. of Mathematics, ().
|
[16] |
J. M. Wozencraft, List decoding, in "Quarterly Progress Report,'' MIT, Cambridge, MA, (1958), 90-95. |
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