Note on the g-fold Joint Weight Enumerators of Self-Dual Codes over ℤ _k

Abstract.

Recently there has been interest in self-dual codes over finite rings. In this note, g-fold joint weight enumerators of codes over the ring ℤ _k of integers modulo k are introduced as a generalization of the biweight enumerators. We establish the MacWilliams relations for these weight enumerators and investigate the biweight enumerators of self-dual codes over ℤ _k . We derive Gleason-type theorems for the corresponding biweight enumerators with the help of invariant theory.