Constructing error-correcting binary codes using transitive permutation groups

Antti Laaksonen*, Patric R.J. Östergård

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

Transitive permutation groups are recurrent in the study of automorphism groups of combinatorial objects. For binary error-correcting codes, groups are here considered that act transitively on the pairs of coordinates and coordinate values. By considering such groups in an exhaustive manner and carrying out computer searches, the following new bounds are obtained on A2(n,d), the maximum size of a binary code of length n and minimum distance d: A2(17,3)≥5632, A2(20,3)≥40960, A2(21,3)≥81920, A2(22,3)≥163840, A2(23,3)≥327680, A2(23,9)≥136, and A2(24,5)≥17920.

Original languageEnglish
Pages (from-to)65-70
JournalDiscrete Applied Mathematics
Volume233
DOIs
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Binary codes
  • Cliques
  • Error-correcting codes
  • Transitive groups

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