کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5771616 | 1630356 | 2017 | 16 صفحه PDF | دانلود رایگان |
- 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.
Journal: Finite Fields and Their Applications - Volume 47, September 2017, Pages 145-160