1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Mathematics, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Sabanci University4 Instituto Nacional de Matematica Pura E Aplicada5 Instituto Nacional de Matematica Pura E Aplicada
In this paper we construct Galois towers with good asymptotic properties over any non-prime finite field Fℓ; i.e., we construct sequences of function fields N=(N1⊂N2⊂⋯) over Fℓ of increasing genus, such that all the extensions Ni/N1 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.
Acta Arithmetica, 2014, Vol 164, Issue 2, p. 163-179