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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Jay A. Wood (2024) studied this question.
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