Improved bounds on weil sums over galois rings and homogeneous weights

Abstract

We generalize a recent improvement for the bounds of Weil sums over Galois rings of characteristic p2 to Galois rings of any characteristic pl. Our generalization is not as strong as for the case p 2 and we indicate the reason. We give a class of homogeneous weights, including the homogeneous weight defined by Constantinescu and Heise, and we show their relations. We also give an application of our improvements on the homogeneous weights of some codewords. © Springer-Verlag Berlin Heidelberg 2006.