Weights modulo p^e of linear codes over rings

Abstract

In this paper we look at linear codes over the Galois ring GR(p^ℓ,m) with the homogeneous weight and we prove that the number of codewords with homogenous weights in a particular residue class modulo p^e are divisible by high powers of p. We also state a result for a more generalized weight on linear codes over Galois rings. We obtain similar results for the Lee weights of linear codes over F₂m+uF₂m and we prove that the results we obtain are best possible. The results that we obtain are an improvement to Wilson's results in [Wilson RM (2003) In: Proceedings of international workshop on Cambridge linear algebra and graph coloring].

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