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On Chebyshev polynomials and maximal curves

100%

Garcia A., Stichtenoth H.

Acta Arithmetica

1999

tom 90

nr 4

301-311

Galois towers over non-prime finite fields

81%

Bassa A., Beelen P., Garcia A., Stichtenoth H.

Acta Arithmetica

2014

tom 164

nr 2

163-179

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.

Ograniczanie wyników

2 Acta Arithmetica

2 Garcia A.

2 Stichtenoth H.

1 Bassa A.

1 Beelen P.

1 2014

1 1999

Wyniki wyszukiwania

On Chebyshev polynomials and maximal curves

Galois towers over non-prime finite fields