Switching of covering codes

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

Organisaatiot

  • Indiana University - Purdue University Indianapolis

Kuvaus

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.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut1778-1788
Sivumäärä11
JulkaisuDiscrete Mathematics
Vuosikerta341
Numero6
Varhainen verkossa julkaisun päivämäärä2017
TilaJulkaistu - kesäkuuta 2018
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 16403285