Publication: Algebraic curves over F-3 with many rational points
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Publication Date
2004
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Springer-Verlag Berlin
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Abstract
We present a method to find curves over the finite field F-3 with many rational points. The method is based in an arithmetic study of linear systems of projective plane curves of a given degree and prescribed singularities. We have found curves of genera 4, 5, 6, 7 and 8 which in the cases of genera 5 and 8 improve the existent bounds for the number of rational points, and in the cases of genera 4, 6 and 7 reach these bounds.
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Conference: Conference on Algebra, Arithmetic, Geometry and its Applications Location: Purdue Univ, W Lafayette, in Date: Jul 20-26, 2000