Geodesic
Galois towers over non-prime finite fields
Alp Bassa 1   ; Peter Beelen 2   ; Arnaldo Garcia 3   ; Henning Stichtenoth 1
1 MDBF Sabancı University 34956 Tuzla, İstanbul, Turkey
2 Department of Applied Mathematics and Computer Science Technical University of Denmark Matematiktorvet, Building 303B DK-2800, Lyngby, Denmark
3 IMPA – Instituto Nacional de Matemática Pura e Aplicada Estrada Dona Castorina 110 22460-320, Rio de Janeiro, RJ, Brazil
Acta Arithmetica, Tome 164 (2014) no. 2, pp. 163-179 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We construct Galois towers with good asymptotic properties over any non-prime finite field $\mathbb F_{\ell }$; that is, we construct sequences of function fields $\mathcal {N}=(N_1 \subset N_2 \subset \cdots )$ over $\mathbb F_{\ell }$ 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.
DOI : 10.4064/aa164-2-6
Keywords: construct galois towers asymptotic properties non prime finite field mathbb ell construct sequences function fields mathcal subset subset cdots mathbb ell increasing genus extensions galois extensions number rational places these function fields grows linearly genus limits towers satisfy lower bounds best currently known lower bounds ihara constant non prime finite fields towers these properties important applications various fields including coding theory cryptography

Alp Bassa  1   ; Peter Beelen  2   ; Arnaldo Garcia  3   ; Henning Stichtenoth  1

1 MDBF Sabancı University 34956 Tuzla, İstanbul, Turkey
2 Department of Applied Mathematics and Computer Science Technical University of Denmark Matematiktorvet, Building 303B DK-2800, Lyngby, Denmark
3 IMPA – Instituto Nacional de Matemática Pura e Aplicada Estrada Dona Castorina 110 22460-320, Rio de Janeiro, RJ, Brazil 
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     title = {Galois towers over non-prime finite fields},
     journal = {Acta Arithmetica},
     pages = {163--179},
     year = {2014},
     volume = {164},
     number = {2},
     doi = {10.4064/aa164-2-6},
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     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa164-2-6/}
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Alp Bassa; Peter Beelen; Arnaldo Garcia; Henning Stichtenoth. Galois towers over non-prime finite fields. Acta Arithmetica, Tome 164 (2014) no. 2, pp. 163-179. doi: 10.4064/aa164-2-6

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