Hess, Florian and Stichtenoth, Henning and Tutdere, Seher (2013) On invariants of towers of function fields over finite fields. Journal of Algebra and Its Applications, 12 (4). ISSN 02194988 (Print) 17936829 (Online)
This is the latest version of this item.
Official URL: http://dx.doi.org/10.1142/S0219498812501903
Abstract
In this paper, we consider a tower of function fields F = (Fn)(n >= 0) over a finite field Fq and a finite extension E/F0 such that the sequence epsilon := E . F = (EFn)(n >= 0) is a tower over the field Fq. Then we study invariants of epsilon, that is, the asymptotic number of the places of degree r in epsilon, for any r >= 1, if those of F are known. We first give a method for constructing towers of function fields over any finite field Fq with finitely many prescribed invariants being positive. For q a square, we prove that with the same method one can also construct towers with at least one positive invariant and certain prescribed invariants being zero. Our method is based on explicit extensions. Moreover, we show the existence of towers over a finite field Fq attaining the DrinfeldVladut bound of order r, for any r >= 1 with q(r) a square (see [1, Problem2]). Finally, we give some examples of nonoptimal recursive towers with all but one invariants equal to zero.
Item Type:  Article 

Additional Information:  Article Number: 1250190 
Uncontrolled Keywords:  Towers of function fields; genus; number of places 
Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences 
Depositing User:  Henning Stichtenoth 
Date Deposited:  23 Jul 2013 11:40 
Last Modified:  01 Aug 2019 10:39 
URI:  https://research.sabanciuniv.edu/id/eprint/21697 
Available Versions of this Item

On invariants of towers of function fields over finite fields. (deposited 14 Oct 2012 00:01)
 On invariants of towers of function fields over finite fields. (deposited 23 Jul 2013 11:40) [Currently Displayed]