scholarly journals Towards a classification of recursive towers of function fields over finite fields

2006 ◽  
Vol 12 (1) ◽  
pp. 56-77 ◽  
Author(s):  
Peter Beelen ◽  
Arnaldo Garcia ◽  
Henning Stichtenoth
Keyword(s):  
Finite Fields ◽  
Function Fields ◽  
Towers Of Function Fields

New Optimal Tame Towers of Function Fields over Small Finite Fields

2002 ◽  
pp. 372-389 ◽  
Author(s):  
Wen-Ching W. Li ◽  
Hiren Maharaj ◽  
Henning Stichtenoth ◽  
Noam D. Elkies
Keyword(s):  
Finite Fields ◽  
Function Fields ◽  
Towers Of Function Fields

scholarly journals A note on towers of function fields over finite fields

1998 ◽  
Vol 26 (11) ◽  
pp. 3737-3741 ◽  
Author(s):  
Ferruh Özbudak ◽  
Michael Thomas
Keyword(s):  
Finite Fields ◽  
Function Fields ◽  
Towers Of Function Fields

scholarly journals ON INVARIANTS OF TOWERS OF FUNCTION FIELDS OVER FINITE FIELDS

2013 ◽  
Vol 12 (04) ◽  
pp. 1250190 ◽  
Author(s):  
FLORIAN HESS ◽  
HENNING STICHTENOTH ◽  
SEHER TUTDERE
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Function Fields ◽  
Finite Extension ◽  
Towers Of Function Fields ◽  
Asymptotic Number ◽  
Tower Of Function Fields

In this paper, we consider a tower of function fields [Formula: see text] over a finite field 𝔽q and a finite extension E/F0 such that the sequence [Formula: see text] is a tower over the field 𝔽q. Then we study invariants of [Formula: see text], that is, the asymptotic number of the places of degree r in [Formula: see text], for any r ≥ 1, if those of [Formula: see text] 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 Drinfeld–Vladut bound of order r, for any r ≥ 1 with qr a square (see [1, Problem-2]). Finally, we give some examples of non-optimal recursive towers with all but one invariants equal to zero.

scholarly journals Towers of Function Fields over Non-prime Finite Fields

2015 ◽  
Vol 15 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Alp Bassa ◽  
Peter Beelen ◽  
Arnaldo Garcia ◽  
Henning Stichtenoth
Keyword(s):  
Finite Fields ◽  
Function Fields ◽  
Towers Of Function Fields

A link between minimal value set polynomials and tamely ramified towers of function fields over finite fields

2021 ◽  
pp. 2250189
Author(s):  
R. Toledano
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Finite Subset ◽  
Function Fields ◽  
Algebraic Closure ◽  
Value Set ◽  
Towers Of Function Fields ◽  
Value Sets

In this paper, we introduce the notions of [Formula: see text]-polynomial and [Formula: see text]-minimal value set polynomial where [Formula: see text] is a polynomial over a finite field [Formula: see text] and [Formula: see text] is a finite subset of an algebraic closure of [Formula: see text]. We study some properties of these polynomials and we prove that the polynomials used by Garcia, Stichtenoth and Thomas in their work on good recursive tame towers are [Formula: see text]-minimal value set polynomials for [Formula: see text], whose [Formula: see text]-value sets can be explicitly computed in terms of the monomial [Formula: see text].

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