Rodríguez Palanquex, María CruzGarcía Villalba, Luis JavierLuengo Velasco, Ignacio2023-06-202023-06-202001S. S. Abhyankar. Algebraic geometry for scientists and engineers. American Mathematical Society. (1990). D. Le Brigand, J. J. Risler. Algorithme de Brill-Noether et codage des codes de Goppa. Publications du laboratoire danalyse numérique. C.N.R.S. A. Cossidente, J. W. P. Hirschfeld, G. Korchmáros, F. Torres. On plane maximal curves. Math. AG/9802113. (Feb. 1998). W. Fulton. Algebraic Curves. An Introduction to Algebraic Geometry. W.A. Bemjamin, Inc., New York. (1969). R. Hartshorne. Algebraic geometry. GTM 76, Springer-Verlag, New York. (1982). M. Namba. Geometry of projective algebraic curves. Marcel Dekker, inc. New York. (1984). H. Stichtenoth. Algebraic Function fields and codes. Springer-Verlag Berlin Heidelberg. (1993). H. Stichtenoth. A note on Hermitian codes over GF(q 2). IEEE Trans. Inf. Theory, vol. 34 (5), pp. 1345–1347. (September 1988). H. J. Tiersma. Remarks on codes from Hermitian curves. IEEE Trans. Inform. Theory, vol. IT-33(4). (July, 1987).0302-974310.1007/3-540-45624-4_19https://hdl.handle.net/20.500.14352/58423This 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.engjournal articlehttp://link.springer.com/chapter/10.1007%2F3-540-45624-4_19http://link.springer.com/restricted access512.7Geometria algebraica1201.01 Geometría Algebraica