Cyclic codes over Rk

Steven T. Dougherty, Suat Karadeniz, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

Cyclic codes over an infinite family of rings are defined. The general properties of cyclic codes over these rings are studied, in particular nontrivial one-generator cyclic codes are characterized. It is also proved that the binary images of cyclic codes over these rings under the natural Gray map are binary quasi-cyclic codes of index 2k . Further, several optimal or near optimal binary codes are obtained from cyclic codes over Rk via this map.

Original languageEnglish (US)
Pages (from-to)113-126
Number of pages14
JournalDesigns, Codes, and Cryptography
Volume63
Issue number1
DOIs
StatePublished - Apr 2012
Externally publishedYes

Keywords

  • Cyclic codes
  • Gray map
  • Optimal codes

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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