On the automorphism group of a family of maximal curves not covered by the Hermitian curve

TL;DR

This paper determines the automorphism groups of specific maximal curves that are not covered by Hermitian curves, providing new insights into their structure and a novel characterization of the GK curve.

Contribution

It computes the automorphism groups of certain maximal curves and offers a new characterization of the GK curve as part of this family.

Findings

Automorphism groups of the curves are explicitly computed.

A new characterization of the GK curve is established.

The curves are shown to be subcovers of the GGS curve.

Abstract

In this paper we compute the automorphism group of the curves $\mathcal{X}_{a,b,n,s}$ and $\mathcal{Y}_{n,s}$ introduced in Tafazolian et al. in 2016 as new examples of maximal curves which cannot be covered by the Hermitian curve. They arise as subcovers of the first generalized GK curve (GGS curve). As a result, a new characterization of the GK curve, as a member of this family, is obtained.