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arXiv · 1204.4355

New curves with many points over small finite fields

Karl Rökaeus
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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.

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Karl Rökaeus. 2012-04-19. New curves with many points over small finite fields. https://arxiv.org/abs/1204.4355

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