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Computing the Genus of a Class of Curves Rodríguez Palanquex, María Cruz García Villalba, Luis Javier Luengo Velasco, Ignacio 512.7 Geometria algebraica 1201.01 Geometría Algebraica 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. 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. DGICYT Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T18:43:13Z 2023-06-20T18:43:13Z 2001 journal article https://hdl.handle.net/20.500.14352/58423 0302-9743 10.1007/3-540-45624-4_19 eng PB97-0284-C02-01 TIC2000-0735 TIC 2000-0737-C03-02 restricted access application/pdf Springer Verlag