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Weights with Maximal Symmetry and Failures of the MacWilliams Identities
April 10, 2024 Β· Declared Dead Β· π arXiv.org
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Authors
Jay A. Wood
arXiv ID
2404.07154
Category
math.RA
Cross-listed
cs.IT
Citations
1
Venue
arXiv.org
Last Checked
3 months ago
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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