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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Exponential sums and Goppa codes. I

Authors: Carlos J. Moreno and Oscar Moreno
Journal: Proc. Amer. Math. Soc. 111 (1991), 523-531
MSC: Primary 11T23; Secondary 11L40, 14G15, 94B40
MathSciNet review: 1028291
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Abstract: A bound is obtained which generalizes the Carlitz-Uchiyama result, based on a theorem of Bombieri and Weil about exponential sums. This new bound is used to estimate the covering radius of long binary Goppa codes. A new lower bound is also derived on the minimum distance of the dual of a binary Goppa code, similar to that for BCH codes. This is an example of the use of a number-theory bound for the problem of the estimation of minimum distance of codes, as posed in research problem 9.9 of Mac Williams and Sloane, The Theory of Error Correcting Codes.

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PII: S 0002-9939(1991)1028291-1
Article copyright: © Copyright 1991 American Mathematical Society

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