publications

On the Weight Enumerators of Duadic and Quadratic Residue Codes

Philippe Gaborit, Carmen-Simona Nedeloaia and Alfred Wassermann
carmen.nedeloaia@inria.fr

IEEE Trans. Inform. Theory, vol. 51, no. 1, pp. 402-407, Jan. 2005.

Abstract

In this paper 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.

KEYWORDS
Duadic codes, quadratic residue code, self-dual code, invariant theory, weight enumerator.