Exponential sums and Goppa codes. I

Moreno, Carlos J.; Moreno, Oscar

doi:10.1090/S0002-9939-1991-1028291-1

Exponential sums and Goppa codes. I
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by Carlos J. Moreno and Oscar Moreno

Proc. Amer. Math. Soc. 111 (1991), 523-531

DOI: https://doi.org/10.1090/S0002-9939-1991-1028291-1

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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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