Codes over Z2m and Jacobi forms of genus n

The relations between the complete weight enumerators in genus n of Type II codes over Z(2m) and Jacobi forms of genus n have been discussed. One derives a map between the invariant spaces of the groups G(2m, n) (or H-2m, n, respectively) and the rings of Jacobi forms (or Siegel modular forms, repectively) of genus n. The MacWilliams identities of the complete weight enumerators in genus n of Type II codes over Z(2m) imply that the complete weight enumerators in genus n of Type II codes over Z(2m) is in the invariant space of the groups G(2m, n). (C) 2001 Academic Press.