Weights modulo p ^e of linear codes over rings

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 script F sign_2m+u script F sign_2m 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].