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Let $R$ be a finite commutative ring. We prove that a MacWilliams typerelation between the m-spotty weight enumerators of a linear code over $R$ andits dual hold, if and only if, $R$ is a Frobenius (equivalently,Quasi-Frobenius) ring, if and only if, the number of maximal ideals and minimalideals 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, wepresent a new and simpler proof for the commutative case of Wood's theoremwhich states that $R$ has a generating character if and only if $R$ is aFrobenius ring.

Finite Commutative Rings with a MacWilliams Type Relation for the m-Spotty Hamming Weight Enumerators