MacWilliams weight enumerator identities for linear codes over Z_k are re-derived via theta functions, extended to arbitrary genus, and linked to cyclotomic-field theta functions for prime k.
MacWilliams identities and matroid polynomi als,
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Codes over Finite Ring $\mathbb{Z}_k$, MacWilliams Identity and Theta Function
MacWilliams weight enumerator identities for linear codes over Z_k are re-derived via theta functions, extended to arbitrary genus, and linked to cyclotomic-field theta functions for prime k.