Two-Point Codes for the Generalized GK curve

In this article we investigate AG codes constructed using the generalized Giulietti-Korchmaros curve. More precisely we consider two-point codes coming from this curve. A special case was considered in [5], where two-point codes coming from the Giulietti-Korchmaros curve were studied. However, even in this special case, our results improve upon what is currently known. Our method builds on the order bound for AG codes, which is why we study several Weierstrass semigroups before stating our results on two-point codes. We find several further improvements upon the MinT tables.