Advances in Geometry
Managing Editor: Grundhöfer, Theo
Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Joswig, Michael / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Penttila, Tim / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard
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A generalization of the Giulietti–Korchmáros maximal curve
1IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brazil. Email: (email)
2Sabancı University, FENS, 34956 Istanbul, Turkey. Email: (email)
3Sabancı University, FENS, 34956 Istanbul, Turkey. Email: (email)
Citation Information: Advances in Geometry. Volume 10, Issue 3, Pages 427–434, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/advgeom.2010.020, April 2010
- Published Online:
We introduce a family of algebraic curves over 𝔽q2n (for an odd n) and show that they are maximal. When n = 3, our curve coincides with the 𝔽q6-maximal curve that has been found by Giulietti and Korchmáros recently. Their curve (i.e., the case n = 3) is the first example of a maximal curve proven not to be covered by the Hermitian curve.
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