Switching of covering codes

Research output: Contribution to journalArticleScientificpeer-review

Researchers

Research units

  • Indiana University-Purdue

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.

Details

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

    Research areas

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

ID: 16403285