On a tower of Garcia and Stichtenoth

In 2003, Garcia and Stichtenoth constructed a recursive tower F = (Fn)n≥0 of algebraic function fields over the finite field Fq , where q = l^r with r ≥ 1 and l 2 is a power of the characteristic of Fq. 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 Fn/Fq 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.