Paper Info
Title
Switching of covering codes.
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.
Year
DOI
Venue
2018
10.1016/j.disc.2017.10.020
Discrete Mathematics
Keywords
Field
DocType
Automorphism group,Covering code,Dominating set,Error-correcting code,Hypercube,Switching
Hamming code,Discrete mathematics,Combinatorics,Concatenated error correction code,Group code,Covering code,Block code,Expander code,Linear code,Reed–Muller code,Mathematics
Journal
Volume
Issue
ISSN
341
6
0012-365X
Citations 
PageRank 
References 
0
0.34
2
Authors
2
Name
Order
Citations
PageRank
Patric R. J. Östergård160970.61
William D. Weakley25610.40