Algebraic Curves over $$ \mathbb{F}_3 $$ with Many Rational Points

Ignacio Luengo and Bartolomé López

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 619-626 from Springer

Abstract: Abstract We present a method to find curves over the finite field $$ \mathbb{F}_3 $$ 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.

Keywords: Singular Point; Rational Point; Algebraic Curf; Valuation Ring; Plane Curf (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_36

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DOI: 10.1007/978-3-642-18487-1_36

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