On the weight enumerators of duadic and quadratic residue codes

In this correspondence, we compute the weight enumerators of various quadratic residue codes over F₂ and F₃, together with certain codes of related families like the duadic and the quadratic double circulant codes. We use a parallel algorithm to find the number of codewords of a given (not too high) weight, from which we deduce by usual classical methods for self-dual and formally self-dual codes over F₂ and F₃ their associated, previously unknown, weight enumerators. We compute weight enumerators for lengths as high as 152 for binary codes and 96 for ternary codes.