A circulant approach to skew-constacyclic codes

Neville Fogarty, Heide Gluesing-Luerssen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We introduce a type of skew-generalized circulant matrices that captures the structure of a skew-polynomial ring F[x;θ] modulo the left ideal generated by a polynomial of the form xn-a. This allows us to develop an approach to skew-constacyclic codes based on skew-generalized circulants. Properties of these circulants are derived, and in particular it is shown that for the code-relevant case the transpose of a skew-generalized circulant is a skew-generalized circulant again. This recovers the well-known result that the dual of a skew-constacyclic code is a skew-constacyclic code again. Special attention is paid to the case where xn-a is central.

Original languageEnglish
Pages (from-to)92-114
Number of pages23
JournalFinite Fields and Their Applications
Volume35
DOIs
StatePublished - Sep 1 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

  • Circulants
  • Linear block codes
  • Skew-cyclic codes
  • Skew-polynomial rings

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering (all)
  • Applied Mathematics

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