On invariants of towers of function fields over finite fields

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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 0219-4988 (Print) 1793-6829 (Online)

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Abstract

In this paper, we consider a tower of function fields F = (F-n)(n >= 0) over a finite field F-q and a finite extension E/F-0 such that the sequence epsilon := E . F = (EFn)(n >= 0) is a tower over the field F-q. 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 F-q 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 F-q attaining the Drinfeld-Vladut bound of order r, for any r >= 1 with q(r) a square (see [1, Problem-2]). Finally, we give some examples of non-optimal 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

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