Classification of all Galois subcovers of the Skabelund maximal curves

Abstract

In 2017 Skabelund constructed two new examples of maximal curves Sq and Rq as covers of the Suzuki and Ree curves, respectively. The resulting Skabelund curves are analogous to the Giulietti-Korchmáros cover of the Hermitian curve. In this paper a complete characterization of all Galois subcovers of the Skabelund curves Sq and Rq 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.