Code Equivalence Characterizes Finite Frobenius Rings
نویسنده
چکیده
In this paper we show that finite rings for which the code equivalence 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
Orthogonality Matrices for Modulesover Finite Frobenius RingsandMacWilliams’ EquivalenceTheorem
MacWilliams’ equivalence theorem states that Hamming isometries between linear codes extend to monomial transformations of the ambient space. One of the most elegant proofs for this result is due to K. P. Bogart et al. (1978, Inform. and Control 37, 19–22) where the invertibility of orthogonality matrices of finite vector spaces is the key step. The present paper revisits this technique in orde...
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