Two-point coordinate rings for GK-curves

Details Two-point coordinate rings for GK-curves Two-point coordinate rings for GK-curves

2010-12-16

arxiv.org/abs/1012.3682v1

Mathematics

Number Theory

16 pages

Scientific paper

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.

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