We construct Galois towers with good asymptotic properties over any non-prime finite field ; that is, we construct sequences of function fields = (N₁ ⊂ N₂ ⊂ ⋯) over of increasing genus, such that all the extensions 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-6,
author = {Alp Bassa and Peter Beelen and Arnaldo Garcia and Henning Stichtenoth},
title = {Galois towers over non-prime finite fields},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {163-179},
zbl = {1320.11104},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-6}
}
Alp Bassa; Peter Beelen; Arnaldo Garcia; Henning Stichtenoth. Galois towers over non-prime finite fields. Acta Arithmetica, Tome 166 (2014) pp. 163-179. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-6/