Switching of covering codes

Patric R.J. Östergård, William D. Weakley*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Switching is a local transformation of a combinatorial structure that does not alter the main parameters. Switching of binary covering codes is studied here. In particular, the well-known transformation of error-correcting codes by adding a parity-check bit and deleting one coordinate is applied to covering codes. Such a transformation is termed a semiflip, and finite products of semiflips are semiautomorphisms. It is shown that for each code length n≥3, the semiautomorphisms are exactly the bijections that preserve the set of r-balls for each radius r. Switching of optimal codes of size at most 7 and of codes attaining K(8,1)=32 is further investigated, and semiautomorphism classes of these codes are found. The paper ends with an application of semiautomorphisms to the theory of normality of covering codes.

Original languageEnglish
Pages (from-to)1778-1788
Number of pages11
JournalDiscrete Mathematics
Volume341
Issue number6
Early online date2017
DOIs
Publication statusPublished - Jun 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Automorphism group
  • Covering code
  • Dominating set
  • Error-correcting code
  • Hypercube
  • Switching

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