Abstract
Recently we obtained a sharpening of the Carlitz Uchiyama bound in characteristic two using Serre's improvement on Weil's estimate of the number of rational points on an algebraic curve over a finite field. In this paper we derive an improvement on a theorem of Bombieri and Weil. This has important applications in the theory of codes; for instance we obtain immediate results concerning the minimum distance of the dual of an arbitrary geometric Goppa code and the minimum distance of reversible BCH codes of length 2 m + 1.
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