Cyclic codes and reducible additive equations

Guneri C., Ozbudak F.

IEEE TRANSACTIONS ON INFORMATION THEORY, vol.53, no.2, pp.848-853, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1109/tit.2006.889001
  • Journal Name: IEEE TRANSACTIONS ON INFORMATION THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.848-853
  • Middle East Technical University Affiliated: Yes

Abstract

We prove a Weil-Serre type bound on the number of solutions of a class of reducible additive equations over finite fields. Using the trace representation of cyclic codes, this enables us to write a general estimate for the weights of cyclic codes. We extend Woffmann's weight bound to a larger classes of cyclic codes. In particular, our result is applicable to any cyclic code over F-p and F-p2, where p is an arbitrary prime. Examples indicate that our bound performs very well against the Bose-Chaudhuri-Hocquenghem (BCH) bound and that it yields the exact minimum distance in some cases.