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On the error distance of extended Reed-Solomon codes
1. | Science and Technology on Information Assurance Laboratory, Beijing, China |
2. | Data Communication Science and Technology Research Institute, Beijing, China |
References:
[1] |
E. Berlekamp and L. Welch, Error correction of algebraic block codes, US Patent Number 4633470, 1986. |
[2] |
A. Cafure, G. Matera and M. Privitelli, Singularities of symmetric hypersurfaces and an application to Reed-Solomon codes, Adv. Math. Commun., 6 (2012), 69-94.
doi: 10.3934/amc.2012.6.69. |
[3] |
Q. Cheng, J. Li and J. Zhuang, On determining deep holes of generalized Reed-Solomon codes, in Algorithms and Computation, Springer, Berlin, 2013, 100-110.
doi: 10.1007/978-3-642-45030-3_10. |
[4] |
Q. Cheng and E. Murray, On deciding deep holes of Reed-Solomon codes, in Proc. TAMC 2007, Springer, 2007, 296-305.
doi: 10.1007/978-3-540-72504-6_27. |
[5] |
Q. Cheng and D. Wan, On the list and bounded distance decodability of Reed-Solomon codes, SIAM J. Comput., 37 (2007), 195-209.
doi: 10.1137/S0097539705447335. |
[6] |
Q. Cheng and D. Wan, Complexity of decoding positive-rate Reed-Solomon codes, IEEE Trans. Inf. Theory, 56 (2010), 5217-5222.
doi: 10.1109/TIT.2010.2060234. |
[7] |
V. Guruswami and M. Sudan, Improved decoding of Reed-Solomon and algebraic-geometry codes, IEEE Trans. Inf. Theory, 45 (1995), 1757-1767.
doi: 10.1109/18.782097. |
[8] |
V. Guruswami and A. Vardy, A Maximum-likelihood decoding of Reed-Solomon codes is NP-Hard, IEEE Trans. Inf. Theory, 51 (2005), 2249-2256.
doi: 10.1109/TIT.2005.850102. |
[9] |
Y. J. Li and D. Wan, On error distance of Reed-Solomon codes, Sci. China Math., 51 (2008), 1982-1988.
doi: 10.1007/s11425-008-0066-3. |
[10] |
J. Y. Li and D. Wan, On the subset sum problem over finite fields, Finite Fields Appl., 14 (2008), 911-929.
doi: 10.1016/j.ffa.2008.05.003. |
[11] |
Q. Liao, On Reed-Solomon Codes, Chinese Ann. Math. Ser. B, 32 (2011), 89-98.
doi: 10.1007/s11401-010-0622-3. |
[12] |
R. Lidl and H. Niederreiter, Finite Fields, 2nd edtion, Cambridge Univ. Press. 1997. |
[13] |
M. Sudan, Decoding of Reed-Solomon codes beyond the error-correction bound , J. Complexity, 13 (2007), 180-193.
doi: 10.1006/jcom.1997.0439. |
[14] |
R. Wu and S. Hong, On deep holes of generalized Reed-Solomon codes,, preprint, ().
|
[15] |
J. Zhang, F. W. Fu and Q. Y. Liao, Deep holes of generalized Reed-Solomon codes (in Chinese), Sci. Sin. Math., 43 (2013), 727-740. |
[16] |
G. Zhu and D. Wan, Computing error distance of Reed-Solomon codes, in Theory and Applications of Models of Computation, Springer, Berlin, 2012, 214-224.
doi: 10.1007/978-3-642-29952-0_24. |
show all references
References:
[1] |
E. Berlekamp and L. Welch, Error correction of algebraic block codes, US Patent Number 4633470, 1986. |
[2] |
A. Cafure, G. Matera and M. Privitelli, Singularities of symmetric hypersurfaces and an application to Reed-Solomon codes, Adv. Math. Commun., 6 (2012), 69-94.
doi: 10.3934/amc.2012.6.69. |
[3] |
Q. Cheng, J. Li and J. Zhuang, On determining deep holes of generalized Reed-Solomon codes, in Algorithms and Computation, Springer, Berlin, 2013, 100-110.
doi: 10.1007/978-3-642-45030-3_10. |
[4] |
Q. Cheng and E. Murray, On deciding deep holes of Reed-Solomon codes, in Proc. TAMC 2007, Springer, 2007, 296-305.
doi: 10.1007/978-3-540-72504-6_27. |
[5] |
Q. Cheng and D. Wan, On the list and bounded distance decodability of Reed-Solomon codes, SIAM J. Comput., 37 (2007), 195-209.
doi: 10.1137/S0097539705447335. |
[6] |
Q. Cheng and D. Wan, Complexity of decoding positive-rate Reed-Solomon codes, IEEE Trans. Inf. Theory, 56 (2010), 5217-5222.
doi: 10.1109/TIT.2010.2060234. |
[7] |
V. Guruswami and M. Sudan, Improved decoding of Reed-Solomon and algebraic-geometry codes, IEEE Trans. Inf. Theory, 45 (1995), 1757-1767.
doi: 10.1109/18.782097. |
[8] |
V. Guruswami and A. Vardy, A Maximum-likelihood decoding of Reed-Solomon codes is NP-Hard, IEEE Trans. Inf. Theory, 51 (2005), 2249-2256.
doi: 10.1109/TIT.2005.850102. |
[9] |
Y. J. Li and D. Wan, On error distance of Reed-Solomon codes, Sci. China Math., 51 (2008), 1982-1988.
doi: 10.1007/s11425-008-0066-3. |
[10] |
J. Y. Li and D. Wan, On the subset sum problem over finite fields, Finite Fields Appl., 14 (2008), 911-929.
doi: 10.1016/j.ffa.2008.05.003. |
[11] |
Q. Liao, On Reed-Solomon Codes, Chinese Ann. Math. Ser. B, 32 (2011), 89-98.
doi: 10.1007/s11401-010-0622-3. |
[12] |
R. Lidl and H. Niederreiter, Finite Fields, 2nd edtion, Cambridge Univ. Press. 1997. |
[13] |
M. Sudan, Decoding of Reed-Solomon codes beyond the error-correction bound , J. Complexity, 13 (2007), 180-193.
doi: 10.1006/jcom.1997.0439. |
[14] |
R. Wu and S. Hong, On deep holes of generalized Reed-Solomon codes,, preprint, ().
|
[15] |
J. Zhang, F. W. Fu and Q. Y. Liao, Deep holes of generalized Reed-Solomon codes (in Chinese), Sci. Sin. Math., 43 (2013), 727-740. |
[16] |
G. Zhu and D. Wan, Computing error distance of Reed-Solomon codes, in Theory and Applications of Models of Computation, Springer, Berlin, 2012, 214-224.
doi: 10.1007/978-3-642-29952-0_24. |
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