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• W2489445788 abstract "Let $R$ be a finite commutative ring. We prove that a MacWilliams type relation between the m-spotty weight enumerators of a linear code over $R$ and its dual hold, if and only if, $R$ is a Frobenius (equivalently, Quasi-Frobenius) ring, if and only if, the number of maximal ideals and minimal ideals of $R$ are the same, if and only if, for every linear code $C$ over $R$, the dual of the dual $C$ is $C$ itself. Also as an intermediate step, we present a new and simpler proof for the commutative case of Wood's theorem which states that $R$ has a generating character if and only if $R$ is a Frobenius ring." @default.
• W2489445788 created "2016-08-23" @default.
• W2489445788 creator A5036637052 @default.
• W2489445788 date "2016-05-10" @default.
• W2489445788 modified "2023-09-27" @default.
• W2489445788 title "Finite Commutative Rings with a MacWilliams Type Relation for the m-Spotty Hamming Weight Enumerators" @default.
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• W2489445788 hasPublicationYear "2016" @default.
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