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

Abstract

We present an upper bound for Weil-type exponential sums over Galois rings of characteristic p2 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 ℤp 2, are also derived. These results lead to an improvement on the estimation of the minimum distance of certain trace codes over ℤp 2 and the bounds on the correlation of certain nonlinear p-ary sequences. © 2004 IEEE.