Optimal Curves of Genus 3 over Finite Fields with Discriminant -19

Details Optimal Curves of Genus 3 over Finite Fields with Discriminant -19 Optimal Curves of Genus 3 over Finite Fields with Discriminant -19

2009-02-11

arxiv.org/abs/0902.1901v2

Mathematics

Algebraic Geometry

table of curves was corrected

Scientific paper

In this work we study the properties of maximal and minimal curves of genus 3 over finite fields with discriminant -19. We prove that any such curve can be given by an explicit equation of certain form. Using these equations we obtain a table of maximal and minimal curves over finite fields with discriminant -19 of cardinality up to 997. We also show that existence of a maximal curve implies that there is no minimal curve and vice versa.

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