On coset weight distributions of the Z(4)-linear Goethals codes

We study the coset weight distributions of two well-known families of codes : the three-error-correcting binary Z(4)-linear Goethals codes of length N = 2(m+l), m greater than or equal to 3 odd, and the Z(4)-linear Goethals co des over Z(4) of length n = N/2 = 2(m). The hard case is the weight distrib utions of cosets of weight 4, To know the weight distribution of the coset of weight 4 we have to know the number of codewords of weight 4 in such a c oset, Alltogether, there are nine different types of cosets of weight 4, Fo r six cases, we give the exact expressions for the number of codewords of w eight 4, and for three other cases, we give such expressions in terms of Kl oosterman sums.