Switching of covering codes

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Switching of covering codes. / Östergård, Patric R.J.; Weakley, William D.

In: Discrete Mathematics, Vol. 341, No. 6, 06.2018, p. 1778-1788.

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Östergård, Patric R.J. ; Weakley, William D. / Switching of covering codes. In: Discrete Mathematics. 2018 ; Vol. 341, No. 6. pp. 1778-1788.

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@article{8782916487994d44845555ae6494180f,
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.",
keywords = "Automorphism group, Covering code, Dominating set, Error-correcting code, Hypercube, Switching",
author = "{\"O}sterg{\aa}rd, {Patric R.J.} and Weakley, {William D.}",
year = "2018",
month = "6",
doi = "10.1016/j.disc.2017.10.020",
language = "English",
volume = "341",
pages = "1778--1788",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "6",

}

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TY - JOUR

T1 - Switching of covering codes

AU - Östergård, Patric R.J.

AU - Weakley, William D.

PY - 2018/6

Y1 - 2018/6

N2 - 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.

AB - 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.

KW - Automorphism group

KW - Covering code

KW - Dominating set

KW - Error-correcting code

KW - Hypercube

KW - Switching

UR - http://www.scopus.com/inward/record.url?scp=85034570723&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2017.10.020

DO - 10.1016/j.disc.2017.10.020

M3 - Article

VL - 341

SP - 1778

EP - 1788

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 6

ER -

ID: 16403285