Abstract

In the paper we give a generalization of two results of two results obtained by García and Stichtenoth  ([G-S]) and use them of 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 abelain p-extensions of the rational function field Fq(x) using the trace operator TrFq/Fp.

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