Two-point coordinate rings for GK-curves

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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.

Original languageEnglish (US)
Article number5695101
Pages (from-to)593-600
Number of pages8
JournalIEEE Transactions on Information Theory
Issue number2
StatePublished - Feb 2011


  • Algebraic geometric codes
  • Weierstrass points
  • maximal curves

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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