Quasi-cyclic codes as cyclic codes over a family of local rings

Steven T. Dougherty; Cristina Fernández-Córdoba; Roger Ten-Valls

doi:https://doi.org/10.1016/j.ffa.2016.04.002

Quasi-cyclic codes as cyclic codes over a family of local rings

Steven T. Dougherty, Cristina Fernández-Córdoba, Roger Ten-Valls

Department of Information and Communications Engineering

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

© 2016 Elsevier Inc. All rights reserved. We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the Hamming space via the Gray map. We use the Gray map to produce optimal linear codes that are quasi-cyclic.

Original language	English
Pages (from-to)	138-149
Journal	Finite Fields and Their Applications
Volume	40
DOIs	https://doi.org/10.1016/j.ffa.2016.04.002
Publication status	Published - 1 Jul 2016

Keywords

Codes over rings
Quasi-cyclic codes

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https://doi.org/10.1016/j.ffa.2016.04.002

https://ddd.uab.cat/record/165927

Cite this

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title = "Quasi-cyclic codes as cyclic codes over a family of local rings",

abstract = "{\textcopyright} 2016 Elsevier Inc. All rights reserved. We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the Hamming space via the Gray map. We use the Gray map to produce optimal linear codes that are quasi-cyclic.",

keywords = "Codes over rings, Quasi-cyclic codes",

author = "Dougherty, {Steven T.} and Cristina Fern{\'a}ndez-C{\'o}rdoba and Roger Ten-Valls",

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T1 - Quasi-cyclic codes as cyclic codes over a family of local rings

AU - Dougherty, Steven T.

AU - Fernández-Córdoba, Cristina

AU - Ten-Valls, Roger

PY - 2016/7/1

Y1 - 2016/7/1

N2 - © 2016 Elsevier Inc. All rights reserved. We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the Hamming space via the Gray map. We use the Gray map to produce optimal linear codes that are quasi-cyclic.

AB - © 2016 Elsevier Inc. All rights reserved. We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the Hamming space via the Gray map. We use the Gray map to produce optimal linear codes that are quasi-cyclic.

KW - Codes over rings

KW - Quasi-cyclic codes

U2 - https://doi.org/10.1016/j.ffa.2016.04.002

DO - https://doi.org/10.1016/j.ffa.2016.04.002

M3 - Article

VL - 40

SP - 138

EP - 149

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

SN - 1071-5797

ER -

Quasi-cyclic codes as cyclic codes over a family of local rings

Abstract

Keywords

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