Optimal Curves of Genus 3 over Finite Fields with Discriminant -19 - Mathematics > Algebraic GeometryReport as inadecuate




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



Author: E.
Alekseenko, S.
Aleshnikov, N.
Markin, A.
Zaytsev


Source: https://arxiv.org/



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