The maximum number of points on a curve of genus eight over the field of four elements

JOURNAL OF NUMBER THEORY

卷:220

Article

关键词: Curve;    Jacobian;    Weil polynomial;    Points;   

DOI  :  10.1016/j.jnt.2020.08.002

来源: Elsevier

【 摘 要 】

The Oesterle bound shows that a curve of genus 8 over the finite field F4 can have at most 24 rational points, and Niederreiter and Xing used class field theory to show that there exists such a curve with 21 points. We improve both of these results: We show that a genus-8 curve over F-4 can have at most 23 rational points, and we provide an example of such a curve with 22 points, namely the curve defined by the two equations y(2) + (x(3) + x + 1)y = x(6) + x(5) + x(4) + x(2) and z(3) = (x + 1)y + x(2). (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free