Turkish Journal of Mathematics
DOI
10.3906/mat-1310-52
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
First Page
384
Last Page
393
Recommended Citation
TUTDERE, SEHER
(2014)
"On a tower of Garcia and Stichtenoth,"
Turkish Journal of Mathematics: Vol. 38:
No.
3, Article 2.
https://doi.org/10.3906/mat-1310-52
Available at:
https://journals.tubitak.gov.tr/math/vol38/iss3/2
