A BOUND ON THE MINIMUM DISTANCE OF QUASI-CYCLIC CODES

Gueneri C., Oezbudak F.

SIAM JOURNAL ON DISCRETE MATHEMATICS, vol.26, no.4, pp.1781-1796, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 4
  • Publication Date: 2012
  • Doi Number: 10.1137/120865823
  • Journal Name: SIAM JOURNAL ON DISCRETE MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1781-1796
  • Keywords: quasi-cyclic code, constituent code, trace representation, ALGEBRAIC STRUCTURE, RATE 1/P
  • Middle East Technical University Affiliated: Yes

Abstract

We give a general lower bound for the minimum distance of q-ary quasi-cyclic codes of length ml and index l, where m is relatively prime to q. The bound involves the minimum distances of constituent codes of length l as well as the minimum distances of certain cyclic codes of length m which are related to the fields over which the constituents are defined. We present examples which show that the bound is sharp in many instances. We also compare the performance of our bound against the bounds of Lally and Esmaeili-Yari.