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Two-Point Coordinate Rings for GK-Curves

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1 Author(s)
Duursma, I.M. ; Dept. of Math., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA

Giulietti and Korchmáros presented new curves with the maximal number of points over a field of size q6. Garcia, Güneri, 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-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.

Published in:

Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 2 )

Date of Publication:

Feb. 2011

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