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Two-Point Codes for the Generalized GK curve
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.Comment: 13 page
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