On the construction of skew quasi-cyclic codes

Taher Abualrub, Ali Ghrayeb, Nuh Aydin, Irfan Siap

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21 Citations (Scopus)

Abstract

In this paper, we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a noncommutative ring called the skew polynomial ring F[x;θ]. After a brief description of the skew polynomial ring F[x;θ], it is shown that skew QC codes are left submodules of the ring Rs l= (F[x;θ]/(x s-1))l. The notions of generator and parity-check polynomials are given. We also introduce the notion of similar polynomials in the ring F[x;θ] and show that parity-check polynomials for skew QC codes are unique up to similarity. Our search results lead to the construction of several new codes with Hamming distances exceeding the Hamming distances of the previously best known linear codes with comparable parameters.

Original languageEnglish
Article number4
Pages (from-to)2081-2090
Number of pages10
JournalIEEE Transactions on Information Theory
Volume56
Issue number5
DOIs
Publication statusPublished - May 2010
Externally publishedYes

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Keywords

  • New codes
  • Quasi-cyclic codes
  • Skew fields

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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