Classification of all Galois subcovers of the Skabelund maximal curves

Abstract

In 2017 Skabelund constructed two new examples of maximal curves $\tilde{\mathcal{S}}_q$ and $\tilde{\mathcal{R}}_q$ as covers of the Suzuki and Ree curves, respectively. The resulting Skabelund curves are analogous to the Giulietti-Korchm\'aros cover of the Hermitian curve. In this paper a complete characterization of all Galois subcovers of the Skabelund curves $\tilde{\mathcal{S}}_q$ and $\tilde{\mathcal{R}}_q$ is given. Calculating the genera of the corresponding curves, we find new additions to the list of known genera of maximal curves over finite fields.