A symmetric Roos bound for linear codes

Iwan M. Duursma, Ruud Pellikaan

Research output: Contribution to journalArticle

Abstract

The van Lint-Wilson AB-method yields a short proof of the Roos bound for the minimum distance of a cyclic code. We use the AB-method to obtain a different bound for the weights of a linear code. In contrast to the Roos bound, the role of the codes A and B in our bound is symmetric. We use the bound to prove the actual minimum distance for a class of dual BCH codes of length q2 - 1 over Fq. We give cyclic codes [63, 38, 16] and [65, 40, 16] over F8 that are better than the known [63, 38, 15] and [65, 40, 15] codes.

Original languageEnglish (US)
Pages (from-to)1677-1688
Number of pages12
JournalJournal of Combinatorial Theory. Series A
Volume113
Issue number8
DOIs
StatePublished - Nov 1 2006

Keywords

  • Cyclic code
  • Dual BCH code
  • Minimum distance bound
  • Roos bound

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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