Two-Point Codes for the Generalised GK curve
Élise Barelli, Peter Beelen, Mrinmoy Datta, Vincent Neiger, Johan Rosenkilde · Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU) · 2018
We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti–Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes coming from the Giulietti–Korchmaros curve (GK). Our results completely cover and in many cases improve on their results, using different techniques, while also supporting any GGK curve. Our method builds on the order bound for AG codes: to enable this, we study certain Weierstrass semigroups. This allows an efficient algorithm for computing our improved bounds. We find several new improvements upon the MinT minimum distance tables.