A Coding-theoretic Characterization of Finite Frobenius Rings
نویسنده
چکیده
In this paper we show that finite rings for which the extension theorem of MacWilliams is valid for Hamming weight must necessarily be Frobenius. This result makes use of a strategy of Dinh and López-Permouth.
منابع مشابه
Duality for Modules over Finite Rings and Applications to Coding Theory
This paper sets a foundation for the study of linear codes over nite rings. The nite Frobenius rings are singled out as the most appropriate for coding theoretic purposes because two classical theorems of MacWilliams, the extension theorem and the MacWilliams identities, generalize from nite elds to nite Frobenius rings. It is over Frobenius rings that certain key identi cations can be made bet...
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