On a tower of Garcia and Stichtenoth

Abstract

In 2003, Garcia and Stichtenoth constructed a recursive tower F = (F-n)(n)>= 0 of algebraic function fields over the finite field IF,, where q = iota(T) with r >= 1 and iota > 2 is a power of the characteristic of F-q. They also gave a lower bound for the limit of this tower. In this paper, we compute the exact value of the genus of the algebraic function field F-n/E-q for each n >= 0. Moreover, we prove that when q = 2(K) with k >= 2, the limit of the tower F attains the lower bound given by Garcia and Stichtenoth.