Long extended BCH codes are spanned by minimum weight words

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3857 LNCS, Issue , 2006, Pages 285-294

  Kaufman, Tali ^a   Litsyn, Simon ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; ERROR CORRECTION; NUMBER THEORY; WORD PROCESSING;

BCH CODES; MINIMUM WEIGHT WORDS; SPANNING; SUBCODES;

ENCODING (SYMBOLS);

EID: 33745665804     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11617983_28     Document Type: Conference Paper

References (33)

1. D. Augot, P. Charpin and N. Sendrier, Studying the locator polynomials of minimum weight codewords of BCH codes, IEEE Trans. Inform. Theory, vol. 38, 3, 1992, pp.960-973.
2. E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, 1968.
3. G. Cohen, S. Litsyn and G. Zémor, On the traveling salesman problem in binary Hamming spaces, IEEE Trans. Inform. Theory, vol. 42, 4, 1996, pp.1274-1276.
4. G. Cohen, I. Honkala, S. Litsyn and A. Lobstein, Covering Codes, Elsevier, 1997.
5. S. D. Cohen, The length of primitive BCH codes with minimal covering radius, Designs, Codes, and Cryptography, vol. 10, 1, 1997, pp.5-16.
6. Ph. Delsarte, J. M. Goethals and F. J. MacWilliams, On generalized Reed-Muller codes and their relatives, Inform, and Control, vol.16, 1970, pp.403-442.
7. Y. Desaki, T. Fujiwara and T. Kasami, The weight distributions of extended binary primitive BCH codes of length 128, IEEE Trans. Inform. Theory, vol. 43, 4, 1997, pp.1364-1371.
8. P. Ding and J. D. Key, Minimum-weight codewords as generators of generalized Reed-Muller codes, IEEE Trans. Inform. Theory, vol. 46, 6, 2000, pp.2152-2158.
9. J. Francke and J. J. H. Meijers, Super-visible codes, Discrete Math. vol. 110, 1-3, 1992, pp.119-134.
10. S. Gao and J. D. Key, Bases of minimum-weight vectors for codes from designs, Finite Fields Appl. vol. 4, 1, 1998), pp.1-15.
11. J. N. Gutie'rrez and H. Tapia-Recillas, A minimum weight basis for the binary Reed-Muller code, Congr. Numer. 154 (2002), 195-199.
12. Handbook of Coding Theory, North Holland, 1997.
13. C. S. Jutla, A. C. Patthak, A. Rudra and D. Zuckerman, Testing low-degree polynomials over prime fields, in book: Proc. IEEE Symposium on Foundations of Computer Science, 2004.
14. T. Kasami, T. Fujiwara, S. Lin, An approximation to the weight distribution of binary linear codes, IEEE Trans. Inform. Theory, vol. 31, 6, 1985, pp.769-780.
15. T. Kaufman and D. Ron, Testing polynomials over general fields, in book: Proc. IEEE Symposium on Foundations of Computer Science, 2004.
16. O. Keren and S. Litsyn, More on the distance distribution of BCH codes, IEEE Trans. Inform. Theory, vol. 45, 1, 1999, pp. 251-255.
17. T. Koumoto, T. Takata, T. Kasami, and S. Lin, A low-weight trellis-based iterative soft-decision decoding algorithm for binary linear block codes, IEEE Trans. Inform. Theory, vol.45, 2, 1999, pp.731-741.
18. I. Krasikov and S. Litsyn, On spectra of BCH codes, IEEE Trans. Inform. Theory, vol.41, 3, 1995, pp.786-788.
19. I. Krasikov and S. Litsyn, Linear programming bounds for codes of small size, European J. Combin., vol.18, 6, 1997), pp.647-654.
20. I. Krasikov, and S. Litsyn, On the distance distributions of BCH codes and their duals, Des. Codes Cryptogr., vol. 23, 2, 2001, pp.223-231.
21. I. Krasikov and S. Litsyn, Survey of binary Krawtchouk polynomials, in book: Codes and Association Schemes, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol.56, 2001, pp. 199-211.
22. F. Levy-dit-Vehel and S. Litsyn, More on the covering radius of BCH codes, IEEE Trans. Inform. Theory, vol. 42, 1996, pp. 1023-1028.
23. F. J. MacWilliams and N. J. A. Sloane. The Theory of Error Correcting Codes. North Holland, 1977.
24. A. W. Marshall and I. Olkin. Inequalities: Theory of Majorization and its Applications. Academic Press, New York, 1979.
25. R. J. McEliece, H. Rumsey.Jr. Sphere-packing in the Hamming metric, Bull. Amer. Math. Soc., vol.75, 1969, pp. 32-34.
26. V. M. Sidel'nikov, The spectrum of weights of binary Bose-Chaudhuri- Hocquenghem codes, Problemy Peredachi Informatsii, vol.7, 1, 1971, pp. 14-22.
27. A. N. Skorobogatov and S. G. Vladuts, The covering radius of long binary BCH codes, Problemy Peredachi Informatsii, vol. 25, 1, 1989, pp.38-45.
28. P. Sole, A limit law on the distance distribution of binary codes, IEEE Trans. Inform. Theory, vol. 36, 1990, pp.229-232.
29. A. Tietäväinen, Bounds for binary codes just outside the Plotkin range, Inform, and Control, vol. 47, 2, 1980, pp.85-93.
30. A. Tietäväinen, On the covering radius of long binary BCH codes, Discr. App. Math., vol. 16, 1987, pp. 75-77.
31. A. Tietäväinen, An asymptotic bound on the covering radius of binary BCH codes, IEEE Trans. Inform. Theory, vol. 36, 1990, pp.211-213.
32. S. Vladuts and A. Skorobogatov, On spectra of subcodes over subfields of algebraicgeometric codes, Probl. Peredachi Inform., vol. 27, 1, 1991, pp.24-36.
33. A. J. van Zanten, Minimal-change order and separability in linear codes, IEEE Trans. Inform. Theory, vol. 39, 6, 1993, pp. 1988-1989.