Galois Towers over Non-prime Finite Fields

Arnaldo Garcia | Alp Bassa | Peter Beelen | Henning Stichtenoth

**Keywords:**towers | curves | finite fields | galois closure | Ihara constant

In this paper we construct Galois towers with good asymptotic properties over any non-

prime finite field F ; i.e., we construct sequences of function fields N = (N1, N2,... )

over F of increasing genus, such that all the extensions Ni over 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.