A multiset approach to MacWilliams identities
Combinatorics
2025-09-26 v1 Information Theory
math.IT
Abstract
We interpret the symmetrized weight enumerator of linear codes over finite commutative Frobenius rings as a summation over multisets and thereby provide a new proof of the MacWilliams identity for the symmetrized weight enumerator. The proof and the identity are expressed in combinatorial terms that do not require generating characters. We also generalize the symmetrized weight enumerator with respect to supports and codeword tuples, and our multiset approach enables us to derive new and general MacWilliams identities expressed in combinatorial terms.
Keywords
Cite
@article{arxiv.2509.20794,
title = {A multiset approach to MacWilliams identities},
author = {Hopein Christofen Tang},
journal= {arXiv preprint arXiv:2509.20794},
year = {2025}
}
Comments
28 pages,4 figures