On the automorphism group of a family of maximal curves not covered by the Hermitian curve (Q6615555)

Maximal curves over \({\mathbb F}_{q}\) (i.e. curves of genus \(g\) which attain the upper Hasse-Weil bound \(q+2g\sqrt{q}+1\) for the number of their \({\mathbb F}_{q}\)-rational points) are objects of wide interest, both for their structure as extremal objects and for their applications to coding theory. Many known maximal curves arise as subcovers of the Hermitian curve. The paper under review considers the curves \({\mathcal X}_{a,b,n,s}\) and \({\mathcal Y}_{n,s}\) introduced by \textit{S. Tafazolian} et al. [J. Pure Appl. Algebra 220, No. 3, 1122--1132 (2016; Zbl 1401.11111)] which arise as subcovers of the Garcia-Güneri-Stichtenoth (GGS) curves in \({\mathbb F}_{q^{2n}}\) and computes in detail their full automorphism group. As a byproduct, a new characterization of the GK curve within this family is obtained.