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International Conference on Algebra and its Applications
March 25-28, 1999
Ohio University
Athens, OH, USA

Organizers
Dinh Van Huynh, S.K. Jain, Sergio Lopez-Permouth

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On Finite Rings Admitting MacWilliams' Equivalence Theorem
by
Marcus Greferath
AT&T Labs-Research, Florham Park, NJ

MacWilliams proved that Hamming isometries between linear codes over finite fields extend to monomial transformations of the ambient vector space and thereby justified the equivalence notion for classical algebraic coding theory. This talk introduces a general inversion principle for real functions on finite modules which allows a combinatorial proof of the equivalence theorem for a class of finite rings that contains all finite Frobenius rings.

http://www.uni-duisburg.de/FB11/STAFF/Greferath.html

Date received: February 22, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabw-84.