Weights with Maximal Symmetry and Failures of the MacWilliams Identities
Rings and Algebras
2025-10-31 v1 Information Theory
math.IT
Abstract
This paper examines the -weight enumerators of weights with maximal symmetry over finite chain rings and matrix rings over finite fields. In many cases, including the homogeneous weight, the MacWilliams identities for -weight enumerators fail because there exist two linear codes with the same -weight enumerator whose dual codes have different -weight enumerators.
Keywords
Cite
@article{arxiv.2404.07154,
title = {Weights with Maximal Symmetry and Failures of the MacWilliams Identities},
author = {Jay A. Wood},
journal= {arXiv preprint arXiv:2404.07154},
year = {2025}
}
Comments
84 pages, 1 figure