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Transactions of the American Mathematical Society

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

 

 

Weight distributions of geometric Goppa codes


Author: Iwan M. Duursma
Journal: Trans. Amer. Math. Soc. 351 (1999), 3609-3639
MSC (1991): Primary 11T71, 14G15, 94B27
DOI: https://doi.org/10.1090/S0002-9947-99-02179-0
Published electronically: May 3, 1999
MathSciNet review: 1473438
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Abstract: The in general hard problem of computing weight distributions of linear codes is considered for the special class of algebraic-geometric codes, defined by Goppa in the early eighties. Known results restrict to codes from elliptic curves. We obtain results for curves of higher genus by expressing the weight distributions in terms of $L$-series. The results include general properties of weight distributions, a method to describe and compute weight distributions, and worked out examples for curves of genus two and three.


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Additional Information

Iwan M. Duursma
Affiliation: AT&T Labs Research, 180 Park Avenue, Florham Park, New Jersey 07932
Address at time of publication: Department of Mathematics, University of Limoges, 123 avenue Albert Thomas, 87060 Limoges, France
Email: duursma@unilin.fr

DOI: https://doi.org/10.1090/S0002-9947-99-02179-0
Keywords: Algebraic curve over a finite field, algebraic-geometric code, weight distribution
Received by editor(s): December 27, 1996
Received by editor(s) in revised form: July 15, 1997
Published electronically: May 3, 1999
Additional Notes: This work was initiated while the author was a post-doc at the CNRS Laboratoire de Mathématiques Discrètes, Luminy, France, with support by the Netherlands Organization for Scientific Research NWO
Article copyright: © Copyright 1999 American Mathematical Society