New curves with many points over small finite fields

被引：1

作者：

Rokaeus, Karl ^{[1
]}

机构：

[1] Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2013年 / 21卷

关键词：

Curves; Rational points;

D O I：

10.1016/j.ffa.2013.01.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use class field theory to search for curves with many rational points over the finite fields of cardinality <= 5. By going through abelian covers of each curve of genus s <= 2 over these fields we find a number of new curves. In particular, over F-2 we settle the question of how many points there can be on a curve of genus 17 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 (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：58 / 66

页数：9

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