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.
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