Dergiler / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 3
On a tower of Garcia and Stichtenoth
- Sayfa
- 384–393
- DOI
- —
Özet
In 2003, Garcia and Stichtenoth constructed a recursive tower F = (Fn)n \geq 0 of algebraic function fields over the finite field Fq, where q = lr with r \geq 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 \geq 0. Moreover, we prove that when q = 2k, with k \geq 2, the limit of the tower F attains the lower bound given by Garcia and Stichtenoth.
Abstract
In 2003, Garcia and Stichtenoth constructed a recursive tower F = (Fn)n \geq 0 of algebraic function fields over the finite field Fq, where q = lr with r \geq 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 \geq 0. Moreover, we prove that when q = 2k, with k \geq 2, the limit of the tower F attains the lower bound given by Garcia and Stichtenoth.