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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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Homogeneous Weights and Gray Isometries for Finite Chain Rings
by
Stefan E. Schmidt
AT&T Labs-Research, Florham Park, NJ
Coauthors: Marcus Greferath

We extend I. Constantinescu's and W. Heise's concept of a homogeneous weight to arbitrary finite rings. For chain rings equipped with this weight we construct isometric embeddings onto first-order generalized Reed-Muller Codes over their residue field. This improves previous results by C. Carlet, I. Constantinescu and A. A. Nechaev. In particular our construction generalizes the fundamental Gray isometry between (Z4, wLee) and (Z22, wH). As an example we produce a ternary (36, 312, 15) code as a Gray image of a 9-ary lift of the ternary Golay Code.

http://math.berkeley.edu/~schmidt

Date received: March 9, 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-92.