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Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales
versão impressa ISSN 0370-3908
Resumo
GARZON R., Álvaro e 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
Palavras-chave
:
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.