Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1310-52
Keywords
Towers of algebraic function fields, genus, number of places
First Page
384
Last Page
393
Recommended Citation
TUTDERE, S (2014). On a tower of Garcia and Stichtenoth. Turkish Journal of Mathematics 38 (3): 384-393. https://doi.org/10.3906/mat-1310-52
