Two-point coordinate rings for GK-curves
Abstract
Giulietti and Korchm\'aros presented new curves with the maximal number of points over a field of size q6. Garcia, G\"uneri, and Stichtenoth extended the construction to curves that are maximal over fields of size q2n, for odd n >= 3. The generalized GK-curves have affine equations xq+x = yq+1 and yq2-yq = zr, for r=(qn+1)/(q+1). We give a new proof for the maximality of the generalized GK-curves and we outline methods to efficiently obtain their two-point coordinate ring.
0