On rank and kernel of some mixed perfect codes

Fabio Pasticci, Thomas Westerbäck*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Mixed perfect 1-error correcting codes and the associated dual codes over the group Z (n, l), Z (n, l) = under(under(Z2 × Z2 × ⋯ × Z2, {presentation form for vertical right curly bracket}), n) × underover(Z, 2, l), n ≥ 1 and l ≥ 2, are investigated. A lower and an upper bound for the rank k of the kernel of mixed perfect 1-error correcting codes in Z (n, l), depending on the rank r of the mixed perfect code and the structure of the corresponding dual code, are given. Due to a general construction of mixed perfect 1-error correcting group codes in Z (n, l), we show that the upper bound is tight for some n, l and r.

Original languageEnglish
Pages (from-to)2763-2774
Number of pages12
JournalDiscrete Mathematics
Volume309
Issue number9
DOIs
Publication statusPublished - 6 May 2009
MoE publication typeA1 Journal article-refereed

Keywords

  • Fourier coefficient
  • Mixed perfect code
  • Rank

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