Galois towers over non-prime finite fields

Alp Bassa, et al. "Galois towers over non-prime finite fields." Acta Arithmetica 164.2 (2014): 163-179. <http://eudml.org/doc/279843>.

@article{AlpBassa2014,
abstract = {We construct Galois towers with good asymptotic properties over any non-prime finite field $_ℓ$; that is, we construct sequences of function fields = (N₁ ⊂ N₂ ⊂ ⋯) over $_ℓ$ of increasing genus, such that all the extensions $N_i/N_1$ are Galois extensions and the number of rational places of these function fields grows linearly with the genus. The limits of the towers satisfy the same lower bounds as the best currently known lower bounds for the Ihara constant for non-prime finite fields. Towers with these properties are important for applications in various fields including coding theory and cryptography.},
author = {Alp Bassa, Peter Beelen, Arnaldo Garcia, Henning Stichtenoth},
journal = {Acta Arithmetica},
keywords = {towers of function fields; Galois closure; genus; rational places; limits of towers},
language = {eng},
number = {2},
pages = {163-179},
title = {Galois towers over non-prime finite fields},
url = {http://eudml.org/doc/279843},
volume = {164},
year = {2014},
}

TY - JOUR
AU - Alp Bassa
AU - Peter Beelen
AU - Arnaldo Garcia
AU - Henning Stichtenoth
TI - Galois towers over non-prime finite fields
JO - Acta Arithmetica
PY - 2014
VL - 164
IS - 2
SP - 163
EP - 179
AB - We construct Galois towers with good asymptotic properties over any non-prime finite field $_ℓ$; that is, we construct sequences of function fields = (N₁ ⊂ N₂ ⊂ ⋯) over $_ℓ$ of increasing genus, such that all the extensions $N_i/N_1$ are Galois extensions and the number of rational places of these function fields grows linearly with the genus. The limits of the towers satisfy the same lower bounds as the best currently known lower bounds for the Ihara constant for non-prime finite fields. Towers with these properties are important for applications in various fields including coding theory and cryptography.
LA - eng
KW - towers of function fields; Galois closure; genus; rational places; limits of towers
UR - http://eudml.org/doc/279843
ER -