Weil-Serre Type Bounds for Cyclic Codes


GÜNERİ C., ÖZBUDAK F.

IEEE TRANSACTIONS ON INFORMATION THEORY, vol.54, no.12, pp.5381-5395, 2008 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 12
  • Publication Date: 2008
  • Doi Number: 10.1109/tit.2008.2006436
  • Title of Journal : IEEE TRANSACTIONS ON INFORMATION THEORY
  • Page Numbers: pp.5381-5395
  • Keywords: Additive polynomials, cyclic code, factorization left greatest common divisor, trace representation, Weil-Serre bound, WEIGHT DISTRIBUTIONS, CURVES

Abstract

We give a new method in order to obtain Weil-Serre type hounds on the minimum distance of arbitrary cyclic codes over F(pe) of length coprime to p, where e >= 1 is an arbitrary integer. In an earlier paper we obtained Weil-Serre type bounds for such codes only when e = 1 or e = 2 using lengthy explicit factorizations, which seems hopeless to generalize. The new method avoids such explicit factorizations and it produces an effective alternative. Using our method we obtain Weil-Serre type bounds in various cases. By examples we show that our bounds perform very well against Bose-Chaudhuri-Hocquenghem (BCH) bound and they yield the exact minimum distance in some cases.