Abstrakti
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.
Alkuperäiskieli | Englanti |
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Sivut | 1778-1788 |
Sivumäärä | 11 |
Julkaisu | Discrete Mathematics |
Vuosikerta | 341 |
Numero | 6 |
Varhainen verkossa julkaisun päivämäärä | 2017 |
DOI - pysyväislinkit | |
Tila | Julkaistu - kesäk. 2018 |
OKM-julkaisutyyppi | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä |