Weierstrass semigroups on the Skabelund maximal curve

Abstract

In [14], D. Skabelund constructed a maximal curve over Fq4 as a cyclic cover of the Suzuki curve. In this paper we explicitly determine the structure of the Weierstrass semigroup at any point P of the Skabelund curve. We show that its Weierstrass points are precisely the Fq4 -rational points. Also we show that among the Weierstrass points, two types of Weierstrass semigroup occur: one for the Fq-rational points, one for the remaining Fq4 -rational points. For each of these two types its Apéry set is computed as well as a set of generators