Cyclic codes over F2+uF2+vF2+uvF 2

Bahattin Yildiz, Suat Karadeniz

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

In this work, we focus on cyclic codes over the ring F2+uF 2+vF2+uvF2, which is not a finite chain ring. We use ideas from group rings and works of AbuAlrub et.al. in (Des Codes Crypt 42:273-287, 2007) to characterize the ring (F2+uF2+vF 2+uvF2)/(xn-1) and cyclic codes of odd length. Some good binary codes are obtained as the images of cyclic codes over F 2+uF2+vF2+uvF2 under two Gray maps that are defined. We also characterize the binary images of cyclic codes over F2+uF2+vF2+uvF2 in general.

Original languageEnglish (US)
Pages (from-to)221-234
Number of pages14
JournalDesigns, Codes, and Cryptography
Volume58
Issue number3
DOIs
StatePublished - Mar 2011
Externally publishedYes

Keywords

  • Cyclic codes
  • Gray maps
  • Homogeneous weight
  • Lee weight
  • Quasi-cyclic codes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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