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Weights with Maximal Symmetry and Failures of the MacWilliams Identities (2404.07154v1)
Published 10 Apr 2024 in math.RA, cs.IT, and math.IT
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.