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

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

doi: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

3 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

Access to Document

10.1016/j.ffa.2016.04.002

Fingerprint Dive into the research topics of 'Quasi-cyclic codes as cyclic codes over a family of local rings'. Together they form a unique fingerprint.

Cite this

@article{a7d9c84f404d4cc4883f6c17e980777b,

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",

year = "2016",

month = jul,

day = "1",

doi = "10.1016/j.ffa.2016.04.002",

language = "English",

volume = "40",

pages = "138--149",

journal = "Finite Fields and Their Applications",

issn = "1071-5797",

publisher = "Academic Press Inc.",

}

TY - JOUR

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 - 10.1016/j.ffa.2016.04.002

DO - 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 -