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
收藏
页码：58 / 66
页数：9
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