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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board Member: Bannai, Eiichi / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 10, Issue 3 (Jan 2010)

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A generalization of the Giulietti–Korchmáros maximal curve

Arnaldo Garcia
  • IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brazil. Email:
/ Cem Güneri / Henning Stichtenoth
Published Online: 2010-04-12 | DOI: https://doi.org/10.1515/advgeom.2010.020

Abstract

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.

About the article

Received: 2008-02-14

Published Online: 2010-04-12

Published in Print: 2010-07-01



Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2010.020. Export Citation

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[1]
Iwan Duursma and Kit-Ho Mak
Bulletin of the Brazilian Mathematical Society, New Series, 2012, Volume 43, Number 3, Page 453
[2]
Robert Guralnick, Beth Malmskog, and Rachel Pries
Journal of Algebra, 2012, Volume 361, Page 92
[3]
Stefania Fanali and Massimo Giulietti
Advances in Geometry, 2012, Volume 12, Number 2

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