Weights with Maximal Symmetry and Failures of the MacWilliams Identities
<|reference_start|>Weights with Maximal Symmetry and Failures of the MacWilliams Identities: 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.<|reference_end|>
@article{wood2024weights,
    title={Weights with Maximal Symmetry and Failures of the MacWilliams Identities},
    author={Jay A. Wood},
    journal={arXiv preprint arXiv:2404.07154},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.07154},
    primaryClass={math.RA cs.IT math.IT}
}