Abstract.
It is known that if a finite ring R is Frobenius then equivalences of linear codes over R are always monomial transformations. Among other results, in this paper we show that the converse of this result holds for finite local and homogeneous semilocal rings. Namely, it is shown that for every finite ring R which is a direct sum of local and homogeneous semilocal subrings, if every Hamming-weight preserving R-linear transformation of a codeC 1 onto a code C 2 is a monomial transformation then R is a Frobenius ring.
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Partially supported by Center of Ring Theory and Applications, Ohio University.
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Quang Dinh, H., López-Permouth, S. On the Equivalence of Codes over Finite Rings. AAECC 15, 37–50 (2004). https://doi.org/10.1007/s00200-004-0149-5
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DOI: https://doi.org/10.1007/s00200-004-0149-5