A multiset approach to MacWilliams identities
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908558344323072 |
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| author | Tang, Hopein Christofen |
| author_facet | Tang, Hopein Christofen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A multiset approach to MacWilliams identities Tang, Hopein Christofen Combinatorics Information Theory 94B05 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. |
| title | A multiset approach to MacWilliams identities |
| topic | Combinatorics Information Theory 94B05 |
| url | https://arxiv.org/abs/2509.20794 |