Two-point coordinate rings for GK-curves [article]

Iwan M. Duursma
2010 arXiv   pre-print
Giulietti and Korchmáros presented new curves with the maximal number of points over a field of size q^6. Garcia, Güneri, and Stichtenoth extended the construction to curves that are maximal over fields of size q^2n, for odd n >= 3. The generalized GK-curves have affine equations x^q+x = y^q+1 and y^q^2-y^q = z^r, for r=(q^n+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.
arXiv:1012.3682v1 fatcat:ui4wmoz4m5fhdbrnwuhn7fsuqy