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Code equivalence characterizes finite Frobenius rings


Author: Jay A. Wood
Journal: Proc. Amer. Math. Soc. 136 (2008), 699-706
MSC (2000): Primary 94B05; Secondary 16D50, 16L60, 16P10.
DOI: https://doi.org/10.1090/S0002-9939-07-09164-2
Published electronically: November 6, 2007
MathSciNet review: 2358511
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Abstract: 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.


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Additional Information

Jay A. Wood
Affiliation: Department of Mathematics, Western Michigan University, 1903 W. Michigan Ave., Kalamazoo, Michigan 49008–5248
Email: jay.wood@wmich.edu

DOI: https://doi.org/10.1090/S0002-9939-07-09164-2
Keywords: Finite Frobenius rings, Hamming weight, equivalence theorem, extension property
Received by editor(s): February 6, 2007
Published electronically: November 6, 2007
Communicated by: Martin Lorenz
Article copyright: © Copyright 2007 American Mathematical Society

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