Computing the Genus of a Class of Curves
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2001
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Springer Verlag
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Abstract
The aim of this paper is to present an exhaustive algebraic study of a new class of curves, the so-called Quasihermitian curves (that includes the Hermitian curves), computing its genus. These curves allow to construct good algebraic geometric Goppa codes since they are absolutely irreducible plane curves with many rational points on Fq.
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This work was supported by DGICYT (Dirección General de Investigación del Ministerio de Ciencia y Tecnología) under grants PB97-0284-C02-01, TIC2000-0735 and TIC 2000-0737-C03-02.
During this work J. Garc´ıa-Villalba was with the IBM Research Division
K65/C2 at IBM Almaden Research Center, San Jose, California, USA (e-mail: javiervi@almaden.ibm.com). J. García-Villalba would like to express his appreciation to the Programa Complutense del Amo for providing him a grant to stay at IBM Almaden Research Center.