Article ID Journal Published Year Pages File Type
5771616 Finite Fields and Their Applications 2017 16 Pages PDF
Abstract

•We study curves of low genus over finite fields with many rational points.•The defect of a curve is the Weil-Serre bound, minus the curve's number of points.•We present algorithms for constructing curves of genus 5, 6, and 7 with small defect.•We implemented our algorithms, and found many record-breaking curves.

The defect of a curve over a finite field is the difference between the number of rational points on the curve and the Weil-Serre upper bound for the number of points on the curve. We present algorithms for constructing curves of genus 5, 6, and 7 with small defect. Our aim is to be able to produce, in a reasonable amount of time, curves that can be used to populate the online table of curves with many points found at manypoints.org.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
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