Some Genus 3 Curves with Many Points

Authors:
Roland Auer;Jaap Top
Affiliations:
-;-
Venue:
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Year:
2002

Citing 1
Cited 1

Nonsingular plane cubic curves over finite fields

Journal of Combinatorial Theory Series A

Twists of genus three curves over finite fields

Finite Fields and Their Applications

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Abstract

We explain a naive approach towards the problem of finding genus 3 curves C over any given finite field Fq of odd characteristic, with a number of rational points close to the Hasse-Weil-Serre upper bound q +1+3[2驴q]. The method turns out to be successful at least in characteristic 3.