Galois towers over non-prime finite fields

• Autorzy: Alp Bassa , Peter Beelen , Arnaldo Garcia , Henning Stichtenoth
• Języki publikacji: EN

Abstrakty

EN

We construct Galois towers with good asymptotic properties over any non-prime finite field $𝔽_ℓ$; that is, we construct sequences of function fields 𝓝 = (N₁ ⊂ N₂ ⊂ ⋯) over $𝔽_ℓ$ 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.

Kategorie tematyczne

• 11G20: Curves over finite and local fields
• 11R32: Galois theory
• 11G09: Drinfel\cprime d modules; higher-dimensional motives, etc.
• 11R58: Arithmetic theory of algebraic function fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 164
• Numer: 2
• Strony: 163-179

Daty

wydano

2014

Twórcy

autor

Alp Bassa

• MDBF, Sabancı University, 34956 Tuzla, İstanbul, Turkey

autor

Peter Beelen

• Department of Applied Mathematics, and Computer Science, Technical University of Denmark, Matematiktorvet, Building 303B, DK-2800, Lyngby, Denmark

autor

Arnaldo Garcia

• IMPA - Instituto Nacional de, Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, RJ, Brazil

autor

Henning Stichtenoth

• MDBF, Sabancı University, 34956 Tuzla, İstanbul, Turkey

Identyfikatory

DOI

10.4064/aa164-2-6