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• # Artykuł - szczegóły

## Acta Arithmetica

2014 | 164 | 2 | 163-179

## Galois towers over non-prime finite fields

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.

163-179

wydano
2014

### Twórcy

autor
• MDBF, Sabancı University, 34956 Tuzla, İstanbul, Turkey
autor
• Department of Applied Mathematics, and Computer Science, Technical University of Denmark, Matematiktorvet, Building 303B, DK-2800, Lyngby, Denmark
autor
• IMPA - Instituto Nacional de, Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, RJ, Brazil
autor
• MDBF, Sabancı University, 34956 Tuzla, İstanbul, Turkey