Optimal Curves of Genus 3 over Finite Fields with Discriminant -19
Algebraic Geometry
2011-08-16 v2 Number Theory
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.
Cite
@article{arxiv.0902.1901,
title = {Optimal Curves of Genus 3 over Finite Fields with Discriminant -19},
author = {E. Alekseenko and S. Aleshnikov and N. Markin and A. Zaytsev},
journal= {arXiv preprint arXiv:0902.1901},
year = {2011}
}
Comments
table of curves was corrected