An improvement on the bounds of Weil exponential sums over Gallois rings with some applications

Ling S., Ozbudak F.

IEEE TRANSACTIONS ON INFORMATION THEORY, vol.50, no.10, pp.2529-2539, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 10
  • Publication Date: 2004
  • Doi Number: 10.1109/tit.2004.834743
  • Journal Name: IEEE TRANSACTIONS ON INFORMATION THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2529-2539
  • Middle East Technical University Affiliated: Yes

Abstract

We present an upper bound for Weil-type exponential sums over Galois rings of characteristic p(2) which improves on the analog of the Weil-Carlitz-Uchiyama bound for Galois rings obtained by Kumar, Helleseth, and Calderbank. A more refined bound, expressed in terms of genera of function fields, and an analog of McEliece's theorem on the divisibility of the homogeneous weights of codewords in trace codes over Z(p)2, are also derived. These results lead to an improvement on the estimation of the minimum distance of certain trace codes over Z(p)2 and the bounds on the correlation of certain nonlinear p-ary sequences.