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

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

Research output: Contribution to journalArticleResearchpeer-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 languageEnglish
Pages (from-to)138-149
JournalFinite Fields and Their Applications
Volume40
DOIs
Publication statusPublished - 1 Jul 2016

Keywords

  • Codes over rings
  • Quasi-cyclic codes

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