Bounds on the Minimum Support Weights

IEEE Transactions on Information Theory

Volumn 41, Issue 2, 1995, Pages 432-440

  Helleseth, Tor ^a   Kløve, Torleiv ^a   Ytrehus, Øyvind ^a   Levenshtein, Vladimir I ^b  

^a UNIVERSITY OF BERGEN   (Norway)

^b KELDYSH INSTITUTE OF APPLIED MATHEMATICS   (Russian Federation)

Author keywords

bounds; Linear codes; support weight

Indexed keywords

COMPUTATIONAL METHODS; INFORMATION THEORY; MATHEMATICAL MODELS; MATRIX ALGEBRA; SET THEORY; THEOREM PROVING;

BOUNDS; GRIESMER BOUNDS; LINEAR CODES; PLOTKIN BOUNDS; SUPPORT WEIGHTS;

CODES (SYMBOLS);

EID: 0029277140     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.370144     Document Type: Article

References (37)

1. H. Chung, “The second generalized Hamming weight of double-error correcting BCH codes and their dual codes,” in Algebraic Algorithms and Error-Correcting Codes Conf. (New Orleans, LA, 1991).
2. —, “The second generalized Hamming weight of double-error correcting BCH codes and their dual codes,” in Lecture Notes in Computer Science, vol. 539. New York: Springer-Verlag, 1991, pp. 118–129.
3. G. Cohen, L. Huguet, and G. Zémor, “Bounds on generalized weights,” in Proc 1st French-Israeli Workshop on Algebraic Coding (Paris, July 1993), Springer LNCS 781, pp. 270–277.
4. I. Duursma, H. Stichtenoth, and C. Voß, “Generalized Hamming weights for duals of BCH codes and maximal algcbraic function fields,” preprint, 1993.
5. S. Encheva and T. Kløve, “Codes satisfying the chain condition,” IEEE Trans. Inform. Theory, vol. 40, pp. 175–180, 1994.
6. G. L. Feng, K. K. Tzeng, and V. K. Wei, “On the generalized Hamming weights of several classes of cyclic codes”, IEEE Trans. Inform. Theory, vol. 38, pp. 1125–1130, 1992.
7. G. D. Forney, “Dimension/length profiles and trellis complexity of linear block codes,” manuscript, Aug. 1993.
8. G. van der Geer and M. van der Vlugt, “On generalized Hamming weights of BCH-codes,” Rep. 92-19, Dept. of Math. and Comput. Sci., Univ. of Amsterdam, Amsterdam, The Netherlands, 1992.
9. —, “The second generalized Hamming weight of BCH(2)⊥,” Rep. 92-93, Dept. of Math. and Comput. Sci., Univ. of Amsterdam, Amsterdam, The Netherlands, 1992.
10. —, “Generalized Hamming weights of Melas codes and dual Melas codes,” Rep. 93-03, Math. Inst., Univ. of Leiden, Leiden, The Netherlands, 1993.
11. —, “Fiber products of Artin-Schreier curves and generalized Hamming weights of codes,” Rep. 93-05, Dept. of Math. and Comput. Sci., Univ. of Amsterdam, Amsterdam, The Netherlands, 1993.
12. —, “Curves over finite fields of characteristic two with many rational points,” Rep. 93-12, Dept. of Math. and Comput. Sci., Univ. of Amsterdam, Amsterdam, The Netherlands, 1993.
13. T. Hellcseth, T. Klève, and J. Mykkeltveit, “The weight distribution of irreducible cyclic codes with block lengths n1(ql − 1)/N),” Discrete Math., vol. 18, pp. 179–211, 1977.
14. T. Helleseth, T. Klève, and Ø. Ytrehus, “Generalized Hamming weights of linear codes,” IEEE Trans. Inform. Theory, vol. 38, pp. 1133–1140, 1992.
15. —, “Codes and the chain condition,” in Proc. Int. Workshop on Algebraic and Combinatorial Coding Theory (Voneshta Voda, Bulgaria June 22–28, 1992), pp. 88–91.
16. —, “Excess sequences of codes and the chain condition,” in Reports in Informatics, no. 65, Dep. of Informatics, Univ. of Bergen, Bergen, Norway, July 1992.
17. —, “Codes, weight hierarchies, and chains,” in Proc. ICCS/ISITA 92 (Singapore, Nov. 16–20, 1992, pp. 608–612.
18. —, “On generalizations of the Griesmer bound,” in Reports in Informatics, no. 87, Dep. of Informatics, Univ. of Bergen, Bergen, Norway, Sept. 1993.
19. T. Helleseth and P. V. Kumar, “On the weight hierarchy of semiprimitive codes,” Discrete Math., to appear.
20. —, “The weight hierarchy of the Kasami codes,” Discrete Math., to appear.
21. J. W. Hirschfeld, M. A. Tsfasman, and S. G. Vladut, “The weight hierarchy of higher-dimensional Hermitian codes,” IEEE Trans. Inform. Theory, vol. 40, pp. 275–278, 1994.
22. F. Jelinek, Probabilistic Information Theory. New York: McGraw-Hill, 1968.
23. G. Kabatianski, “On second generalized Hamming weight,” in Proc. Int. Workshop on Algebraic and Combinatorial Coding Theory (Voneshta Voda, Bulgaria June 22–28, 1992), pp. 98–100.
24. T. Kløve, “The weight distribution of linear codes over GF(q1) having generator matrix over GF(q),” Discrete Math., vol. 23, pp. 159–168, 1978.
25. —, “Support weight distribution of linear codes,” Discrete Math., vol. 106/107, pp. 311–316, 1992.
26. —, “Minimum support weights of binary codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 648–654, 1993.
27. J. H. van Lint, Introduction to Coding Theory. New York: Springer-Verlag, 1982.
28. D. Nogin, “Generalized Hamming weights for codes on multidimensional quadrics,” Probl. Inform. Transmission, vol. 29, no. 3, pp. 218–227, 1994.
29. J. N. Pierce, “Limit distribution of the minimum distance of random linear codcs,” IEEE Trans. Inform. Theory, vol. IT-13, pp. 595–599, 1967.
30. J. Simonis, “The effective length of subcodes,” manuscript, 1992.
31. H. Stichtenoth and C. Voß, “Generalized Hamming weights of trace codes,” manuscript, 1993.
32. M. van der Vlugt, “On generalized Hamming weights of Melas codes,” Rep., Math. Inst., Univ. of Leiden, leiden, The Netherlands, Oct. 1992.
33. —, “On the weight hierarchy of irreducible cyclic codes,” Rep. W93-15, Math. Inst., Univ. of Leiden, Leiden, The Netherlands, 1993.
34. Z. Wan, “The weight hierarchies of the projective codes from nondegenerate quadrics,” Des., Codes and Cryptogr., vol. 4, pp. 283–300, 1994.
35. V. K. Wei, “Generalized Hamming weights for linear codes,” IEEE Trans. Inform. Theory, vol. 37, pp. 1412–1418, 1991.
36. V. K. Wei and K. Yang, “On the generalized Hamming weights of product codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 1709–1713, 1993.
37. K. Yang, P. V. Kumar, and H. Stichtenoth, “On the weight hierarchy of geometric Goppa codes,” preprint, 1992.