On the existence of extended perfect binary codes with trivial symmetry group

Olof Heden*, Fabio Pasticci, Thomas Westerbäck

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)

Abstract

The set of permutations of the coordinate set that maps a perfect code C into itself is called the symmetry group of C and is denoted by Sym(C). It is proved that for all integers n = 2m - 1, where m = 4, 5, 6, . . . , and for any integer r, where n - log(n + 1) + 3≤ r≤ n - 1, there are perfect codes of length n and rank r with a trivial symmetry group, i.e. Sym(C) = {id}. The result is shown to be true, more generally, for the extended perfect codes of length n + 1.

Original languageEnglish
Pages (from-to)295-309
Number of pages15
JournalAdvances in Mathematics of Communications
Volume3
Issue number3
DOIs
Publication statusPublished - Aug 2009
MoE publication typeA1 Journal article-refereed

Keywords

  • Perfect codes
  • Symmetry group

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