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

Abstract

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.

arXiv commenttable of curves was corrected

Cited by in corpus (2)

• Explicit computations of Serre's obstruction for genus 3 curves and application to optimal curves
• Optimal curves of genus 1,2 and 3