2000 character limit reached
Weights with Maximal Symmetry and Failures of the MacWilliams Identities
Published 10 Apr 2024 in math.RA, cs.IT, and math.IT | (2404.07154v1)
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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.