Homogeneous weight enumerators over integer residue rings and failures of the MacWilliams identities
DOI:
https://doi.org/10.33044/revuma.2807Abstract
The MacWilliams identities for the homogeneous weight enumerator over $\mathbb{Z}/m\mathbb{Z}$ do not hold for composite $m \geq 6$. For such $m$, there exist two linear codes over $\mathbb{Z}/m\mathbb{Z}$ that have the same homogeneous weight enumerator, yet whose dual codes have different homogeneous weight enumerators.
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