Weights with Maximal Symmetry and Failures of the MacWilliams Identities
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2024
- DOI:
- 10.48550/arXiv.2404.07154
- arXiv:
- arXiv:2404.07154
- Bibcode:
- 2024arXiv240407154W
- Keywords:
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- Mathematics - Rings and Algebras;
- Computer Science - Information Theory;
- 94B05
- E-Print:
- 84 pages, 1 figure