Two-point coordinate rings for GK-curves
Number Theory
2010-12-17 v1
Abstract
Giulietti and Korchm\'aros presented new curves with the maximal number of points over a field of size q^6. Garcia, G\"uneri, 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.
Cite
@article{arxiv.1012.3682,
title = {Two-point coordinate rings for GK-curves},
author = {Iwan M. Duursma},
journal= {arXiv preprint arXiv:1012.3682},
year = {2010}
}
Comments
16 pages