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arXiv · 2404.07154

Weights with Maximal Symmetry and Failures of the MacWilliams Identities

Jay A. Wood
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Abstract

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.

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Jay A. Wood. 2024-04-10. Weights with Maximal Symmetry and Failures of the MacWilliams Identities. https://doi.org/10.1090/conm%2F826%2F16588

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