On a tower of Garcia and Stichtenoth

Authors: SEHER TUTDERE

Abstract: In 2003, Garcia and Stichtenoth constructed a recursive tower F = (F_n)_{n \geq 0} of algebraic function fields over the finite field F_q, where q = l^r with r \geq 1 and l > 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/F_q for each n \geq 0. Moreover, we prove that when q = 2^k, with k \geq 2, the limit of the tower F attains the lower bound given by Garcia and Stichtenoth.

Keywords: Towers of algebraic function fields, genus, number of places

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