Abstract

GARZON R., Álvaro  and  TEHERA HERRERA, Arnoldo. ELEMENTARY ABELIAN P-EXTENSIONS AND CURVES WITH MANY POINTS. Rev. acad. colomb. cienc. exact. fis. nat. [online]. 2012, vol.36, n.139, pp.243-252. ISSN 0370-3908.

In this paper we give a generalization of two results obtained by Garcia and Stichtenoth and use them to exhibit a method to construct curves over finite fields whose number of rational points is large compared to their genus. Such curves are induced by algebraic functions fields obtained from elementary abelian -extensions of the rational function field using the trace operator

Keywords : Finite Fields; Algebraic Curves; Algebraic Function Fields; Elementary Abelian -Extensions; Rational Points; Cuerpos finitos; curvas algebraicas; cuerpos algebraicos de funciones; -extensions abelianas elementales; puntos racionales.

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