Giulietti and Korchmros presented new curves with the maximal number of points over a field of size q6. Garcia, Gneri, 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 xq+x = yq+1 and yq2-y = 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.
- Algebraic geometric codes
- Weierstrass points
- maximal curves
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences