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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Euclidean weights of codes from elliptic curves over rings


Authors: José Felipe Voloch and Judy L. Walker
Journal: Trans. Amer. Math. Soc. 352 (2000), 5063-5076
MSC (1991): Primary 94B27; Secondary 11T71, 11G07
Published electronically: June 28, 2000
MathSciNet review: 1778505
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Abstract | References | Similar Articles | Additional Information

Abstract:

We construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools, notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves. These results may be of independent interest.


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Additional Information

José Felipe Voloch
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
Email: voloch@math.utexas.edu

Judy L. Walker
Affiliation: Department of Mathematics and Statistics, University of Nebraska, Lincoln, Nebraska 68588-0323
Email: jwalker@math.unl.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02637-4
PII: S 0002-9947(00)02637-4
Received by editor(s): October 29, 1998
Received by editor(s) in revised form: September 16, 1999
Published electronically: June 28, 2000
Additional Notes: The first author was supported in part by NSA Grant #MDA904-97-1-0037.
The second author was supported in part by NSF Grant #DMS-9709388.
Article copyright: © Copyright 2000 American Mathematical Society