On the coset weight distributions of the Z4-linear Goethals codes

We examine here the coset weight distributions of the two classes of codes: Z₄-linear Goethals codes (which we denote G₄ ) over Z₄ with Lee minimum distance 8, of length n=2 ^m (n odd) and binary Z₄-linear Goethals codes (which we denote G₂) with Hamming minimum distance 8, of length N=2n=2^m+1. We show that the number of distinct weight distributions, for cosets of weight four, increases with the length