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Algebraic curves over F-3 with many rational points

Luengo Velasco, Ignacio and López, Bartolomé (2004) Algebraic curves over F-3 with many rational points. In Algebra, Arithmetic and Geometry with Applications. Springer-Verlag Berlin, Berlin, pp. 619-626. ISBN 3-540-00475-0

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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.


Item Type:Book Section
Additional Information:

Conference: Conference on Algebra, Arithmetic, Geometry and its Applications Location: Purdue Univ, W Lafayette, in Date: Jul 20-26, 2000

Uncontrolled Keywords:Codes
Subjects:Sciences > Mathematics > Algebra
ID Code:16640
Deposited On:11 Oct 2012 08:58
Last Modified:11 Oct 2012 08:58

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