Correcting errors and erasures via the syndrome variety

Journal of Pure and Applied Algebra

Volumn 200, Issue 1-2, 2005, Pages 191-226

  Orsini, Emmanuela ^a   Sala, Massimiliano ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 19544362860     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpaa.2004.12.027     Document Type: Article

References (23)

1. D. Augot, M. Bardet, J.-C. Faugere, Efficient decoding of cyclic codes above the correction capacity of the code using Gröbner bases, ISIT: IEEE International Symposium on Information Theory, 2003.
2. R. Brualdi, W.C. Huffman, V. Pless, Handbook of Coding Theory, Elsevier, Amsterdam, 1998, pp. 649-754.
3. M. Caboara T. Mora The Chen-Reed-Helleseth-Truong decoding algorithm and the Gianni-Kalkbrenner Gröbner shape theorem Appl. Algeb. Eng. Commun. Comput. 13 2002 209-232
4. M. Caboara, T. Mora, E. Orsini, M. Sala, Fast decoding of cyclic codes via the syndrome variety, to appear.
5. G. Castagnoli J.L. Massey P. Schoeller On repeated-root cyclic codes IEEE Trans. Inform. Theory 37 2 1991 337-342
6. X. Chen I.S. Reed T. Helleseth K. Truong Use of Gröbner bases to decode binary cyclic codes up to the true minimum distance IEEE Trans. Inform. Theory 40 1994 1654-1661
7. X. Chen I.S. Reed T. Helleseth T.K. Truong Algebraic decoding of cyclic codes: A polynomial Ideal Point of View Contemporary Math. 168 1994 15-22
8. J.C. Faugère P. Gianni D. Lazard T. Mora Efficient computation of zero-dimensional Gröbner bases by change of ordering J. Symbolic Comput. 16 4 1993 329-344
9. P. Fitzpatrick On the key equation IEEE Trans. Inform. Theory 41 1995 1290-1302
10. G.D. Forney Jr. On decoding BCH Codes IEEE Trans. Inform. Theory 10 1965 549-557
11. E. Fortuna, P. Gianni, B. Trager, Structure of zero-dimensional ideals, to appear.
12. P. Gianni, Properties of Gröbner bases under specialization, Lecture Notes in Computer Science, vol. 378, Springer, Berlin, Heidelberg, New York, 1989, pp. 293-297.
13. M. Kalkbrenner, Solving system of algebraic equation using Gröbner bases, Lecture Notes in Computer Science, vol. 378, Springer, Berlin, Heidelberg, New York, 1989, pp. 282-292.
14. S. Lin E.J. Weldon Jr. Long BCH codes are bad Inform. Control 11 4 1967 445-451
15. P. Loustaunau E.V. York On the decoding of cyclic codes using Gröbner bases Appl. Algeb. Eng. Commun. Comput. 8 6 1997 469-483
16. F.J. MacWilliams N.J.A. Sloane The Theory of Error-Correcting Codes 1977 North-Holland Amsterdam
17. T. Mora M. Sala On the Gröbner bases for some symmetric systems and their application to coding theory J. Scientific Comput. 35 2003 177-194
18. H. O'Keeffe, P. Fitzpatrick, Gröbner basis solution of constrained interpolation problems, Lin. Alg. Appl., 2002, 533-551.
19. W.W. Peterson E.J. Weldon Jr. Error Correcting Codes 1972 MIT Press Cambridge, MA
20. M. Sala Gröbner bases and distance of cyclic codes Appl. Algeb. Eng. Commun. Comput. 13 2 2002 137-162
21. M. Sala, A Gröbner basis technique to compute distance and weight distribution of cyclic codes and their shortened codes, BCRI Preprint Series, No. 10, 2003.
22. M. Sala, General error locator polynomials for linear codes, to appear.
23. J.H. Van Lint Repeated-root cyclic codes IEEE Trans. Inform. Theory 37 2 1991 343-345