论文标题
在四个元素的场上，八属属曲线上的最大点数
The maximum number of points on a curve of genus eight over the field of four elements
论文作者
论文摘要
Oesterlé结合表明，有限场上$ \ mathbb {f} _4 $的属8属曲线最多可以具有24个理性点，而Niederreiter和Xing使用了类字段理论，以表明存在21点的曲线。 We improve both of these results: We show that a genus-8 curve over $\mathbb{F}_4$ 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 $z^3 = (x+1)y + x^2.$
The Oesterlé bound shows that a curve of genus 8 over the finite field $\mathbb{F}_4$ 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 $\mathbb{F}_4$ 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 $z^3 = (x+1)y + x^2.$
