Minimum weight codewords in dual Algebraic-Geometric codes from the Giulietti-Korchm\'aros curve

In this paper we investigate the number of minimum weight codewords of some dual Algebraic-Geometric codes associated with the Giulietti-Korchm'aros maximal curve, by computing the maximal number of intersections between the Giulietti-Korchm'aros curve and lines, plane conics and plane cubics.