Note on the g-fold joint weight enumerators of self-dual codes over Z(k)
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 module 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.
g-fold joint weight enumerators self-dual codes macwilliams relations