Permutation groups and binary self-orthogonal codes

Naoki Chigira, Masaaki Harada, Masaaki Kitazume

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Let G be a permutation group on an n-element set Ω. We study the binary code C (G, Ω) defined as the dual code of the code spanned by the sets of fixed points of involutions of G. We show that any G-invariant self-orthogonal code of length n is contained in C (G, Ω). Many self-orthogonal codes related to sporadic simple groups, including the extended Golay code, are obtained as C (G, Ω). Some new self-dual codes invariant under sporadic almost simple groups are constructed.

Original languageEnglish
Pages (from-to)610-621
Number of pages12
JournalJournal of Algebra
Volume309
Issue number2
DOIs
Publication statusPublished - 2007 Mar 15
Externally publishedYes

Keywords

  • Permutation group
  • Self-orthogonal code and self-dual code
  • Sporadic simple group

ASJC Scopus subject areas

  • Algebra and Number Theory

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