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Galois towers over non-prime finite fields

Volume 164 / 2014

Alp Bassa, Peter Beelen, Arnaldo Garcia, Henning Stichtenoth Acta Arithmetica 164 (2014), 163-179 MSC: 11R32, 11R58, 11G20, 11G09. DOI: 10.4064/aa164-2-6

Abstract

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.

Authors

  • Alp BassaMDBF
    Sabancı University
    34956 Tuzla, İstanbul, Turkey
    e-mail
  • Peter BeelenDepartment of Applied Mathematics
    and Computer Science
    Technical University of Denmark
    Matematiktorvet, Building 303B
    DK-2800, Lyngby, Denmark
    e-mail
  • Arnaldo GarciaIMPA – Instituto Nacional de
    Matemática Pura e Aplicada
    Estrada Dona Castorina 110
    22460-320, Rio de Janeiro, RJ, Brazil
    e-mail
  • Henning StichtenothMDBF
    Sabancı University
    34956 Tuzla, İstanbul, Turkey
    e-mail

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