On a tower of Garcia and Stichtenoth
Authors : Seher Tutdere
Pages : 384-393
Doi:10.3906/mat-1310-52
View : 9 | Download : 8
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Towers of algebraic function fields, genus, number of places