On subfields of the Hermitian function field involving the involution automorphism

JOURNAL OF NUMBER THEORY

卷:198

Article

Ma, Liming¹  Xing, Chaoping² 

[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China

[2] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

关键词: Hermitian function field;    Maximal function fields;    Automorphism groups;    Involution;   

DOI  :  10.1016/j.jnt.2018.10.014

来源: Elsevier

【 摘 要 】

A function field over a finite field is called maximal if it achieves the Hasse-Weil bound. Finding possible genera that maximal function fields can achieve has both theoretical interest and practical applications to coding theory and other topics. As a subfield of a maximal function field is also maximal, one way to find maximal function fields is to find all subfields of a maximal function field. Due to the large automorphism group of the Hermitian function field, it is natural to find as many subfields of the Hermitian function field as possible. In literature, most of papers studied subfields fixed by subgroups of the decomposition group at one point (usually the point at infinity). This is because it becomes much more complicated to study the subfield fixed by a subgroup that is not contained in the decomposition group at one point. In this paper, we study subfields of the Hermitian function field fixed by subgroups that are not contained in the decomposition group of any point except the cyclic subgroups. It turns out that some new maximal function fields are found. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free