ON MAXIMAL CURVES OVER FINITE FIELDS OF SMALL ORDER

被引：5

作者：

Fanali, Stefania ^{[1
]}

Giulietti, Massimo ^{[2
]}

Platoni, Irene ^{[3
]}

机构：

[1] Univ Basilicata, Dipartimento Matemat & Informat, I-85100 Potenza, Italy

[2] Univ Perugia, Dipartimento Matemat & Informat, I-06123 Perugia, Italy

[3] Univ Trento, Dipartimento Matemat, I-38123 Povo, TN, Italy

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2012年 / 6卷 / 01期

关键词：

Maximal curve; AG-codes; Frobenius dimension; Hermitian variety; GENUS;

D O I：

10.3934/amc.2012.6.107

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We show that there exists a unique maximal curve of genus 7 over the finite field with 49 elements, up to birational equivalence. This was the first open classification problem for maximal curves, since maximal curves over the finite fields with less than 49 elements, as well as maximal curves over the finite field with 49 elements with genus larger than 7, had been previously classified. A significant role is played by some exhaustive computer searches.

引用

页码：107 / 120

页数：14

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