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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Euclidean weights of codes from elliptic curves over rings
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by José Felipe Voloch and Judy L. Walker PDF
Trans. Amer. Math. Soc. 352 (2000), 5063-5076 Request permission

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
  • MR Author ID: 179265
  • ORCID: 0000-0003-1669-9306
  • 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
  • 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.
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 5063-5076
  • MSC (1991): Primary 94B27; Secondary 11T71, 11G07
  • DOI: https://doi.org/10.1090/S0002-9947-00-02637-4
  • MathSciNet review: 1778505