Weights with Maximal Symmetry and Failures of the MacWilliams Identities
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914122323460096 |
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| author | Wood, Jay A. |
| author_facet | Wood, Jay A. |
| contents | This paper examines the $w$-weight enumerators of weights $w$ with maximal symmetry over finite chain rings and matrix rings over finite fields. In many cases, including the homogeneous weight, the MacWilliams identities for $w$-weight enumerators fail because there exist two linear codes with the same $w$-weight enumerator whose dual codes have different $w$-weight enumerators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07154 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weights with Maximal Symmetry and Failures of the MacWilliams Identities Wood, Jay A. Rings and Algebras Information Theory 94B05 This paper examines the $w$-weight enumerators of weights $w$ with maximal symmetry over finite chain rings and matrix rings over finite fields. In many cases, including the homogeneous weight, the MacWilliams identities for $w$-weight enumerators fail because there exist two linear codes with the same $w$-weight enumerator whose dual codes have different $w$-weight enumerators. |
| title | Weights with Maximal Symmetry and Failures of the MacWilliams Identities |
| topic | Rings and Algebras Information Theory 94B05 |
| url | https://arxiv.org/abs/2404.07154 |