A relation between quasi-cyclic codes and 2-D cyclic codes

Guneri C., ÖZBUDAK F.

FINITE FIELDS AND THEIR APPLICATIONS, vol.18, no.1, pp.123-132, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2012
  • Doi Number: 10.1016/j.ffa.2011.07.004
  • Journal Name: FINITE FIELDS AND THEIR APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.123-132
  • Keywords: Quasi-cyclic code, 2-D cyclic code, Trace representation, ALGEBRAIC STRUCTURE, FINITE-FIELDS, RATE 1/P
  • Middle East Technical University Affiliated: Yes

Abstract

We consider a q-ary quasi-cyclic code C of length ml and index l, where both in and l are relatively prime to q. If the constituents of C are cyclic codes, we show that C can also be viewed as a 2-D cyclic code of size m x l over F(q). In case in and l are also coprime to each other, we easily observe that the code C must be equivalent to a cyclic code, which was proved earlier by Lim. (C) 2011 Elsevier Inc. All rights reserved.