One generator quasi-cyclic codes over F 2+uF 2

Irfan Siap, Taher Abualrub, Bahattin Yildiz

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

In this paper, we study quasi-cyclic codes over the ring R=F 2u+F 2=0,1,u,u1 where u 2=0. By exploring their structure, we determine the type of one generator quasi-cyclic codes over R and the size by giving a minimal spanning set. We also determine the rank and introduce a lower bound for the minimum distance of free quasi-cyclic codes over R. We include some examples of quasi-cyclic codes of various lengths over R. In particular, we obtain a family of 2-quasi-cyclic codes from cyclic codes over the ring F 2u+F 2v+F 2+uvF 2. Finally, using the Gray map we obtain a family of optimal binary linear codes as the images of quasi-cyclic codes over R.

Original languageEnglish (US)
Pages (from-to)284-292
Number of pages9
JournalJournal of the Franklin Institute
Volume349
Issue number1
DOIs
StatePublished - Feb 2012
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Applied Mathematics

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