# Weierstrass semigroups at every point of the Suzuki curve

Abstract

In this article we explicitly determine the structure of the Weierstrass semigroups H(P)for any point Pof the Suzuki curve \mathcal{S}_q As the point Pvaries, exactly two possibilities arise for H(P) one for the \mathbb{F}_qrational points (already known in the literature), and one for all remaining points. For this last case a minimal set of generators of H(P)is also provided. As an application, we construct dual one-point codes from an \mathbb{F}_{q^4}\setminus\fqpoint whose parameters are better in some cases than the ones constructed in a similar way from an \fqrational point.