New curves with many points over small finite fields
Number Theory
2014-03-12 v2
Abstract
We use class field theory to search for curves with many rational points over small finite fields. By going through abelian covers of curves of small genus we find a number of new curves. In particular, we settle the question of how many points a curve over GF(2) of genus 17 can have, by finding one with 18 points. The search is aided by computer; in some cases it is exhaustive for this type of curve of genus up to 50.
Cite
@article{arxiv.1204.4355,
title = {New curves with many points over small finite fields},
author = {Karl Rökaeus},
journal= {arXiv preprint arXiv:1204.4355},
year = {2014}
}