Improved Bounds on Weil Sums over Galois Rings and Homogeneous Weights
We generalize a recent improvement for the bounds of Weil sums over Galois rings of characteristic p 2 to Galois rings of any characteristic p l . 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.
KeywordsCyclic Code Arithmetic Code Galois Ring Improve Bound Homogeneous Weight
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