Galois towers over non-prime finite fields
Bassa, Alp and Beelen, Peter and Garcia, Arnaldo and Stichtenoth, Henning (2014) Galois towers over non-prime finite fields. Acta Arithmetica, 164 (2). pp. 163-179. ISSN 0065-1036 (Print) 1730-6264 (Online)
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Official URL: http://dx.doi.org/10.4064/aa164-2-6
We construct Galois towers with good asymptotic properties over any non-prime finite field Fℓ; that is, 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.
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