Two-point coordinate rings for GK-curves

Iwan M. Duursma

doi:10.1109/TIT.2010.2095230

Two-point coordinate rings for GK-curves

Research output: Contribution to journal › Article › peer-review

Abstract

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 x^q+x = y^q+1 and y^q2-y = z^r, 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.

Original language	English (US)
Article number	5695101
Pages (from-to)	593-600
Number of pages	8
Journal	IEEE Transactions on Information Theory
Volume	57
Issue number	2
DOIs	https://doi.org/10.1109/TIT.2010.2095230
State	Published - Feb 2011

Keywords

Algebraic geometric codes
Weierstrass points
maximal curves

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2010.2095230

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AB - 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.

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Two-point coordinate rings for GK-curves

Abstract

Keywords

ASJC Scopus subject areas

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