A note on towers of function fields over finite fields
نویسندگان
چکیده
منابع مشابه
Towers of Function Fields over Non-prime Finite Fields
Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(`), for ` = p with p prime and n > 3 odd. A modular interpretation of the towers is given as well.
متن کاملOn the Asymptotic Behaviour of Some Towers of Function Fields over Finite Fields
Let F Fl be an algebraic function field of one variable, whose constant field is the finite field of cardinality l. Weil's theorem states that the number N=N(F ) of places of degree one of F Fl satisfies the estimate N l+1+2g l , (0.1) where g= g(F ) denotes the genus of F. It is well known that for g large with respect to l, the Weil bound (0.1) is not optimal; see [5, 9]. Drinfeld and Vladut ...
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We consider a tower of function fields F = (Fn)n≥0 over a finite field Fq and a finite extension E/F0 such that the sequence E := E ·F = (EFn)n≥0 is a tower over the field Fq. Then we deal with the following: What can we say about the invariants of E ; i.e., the asymptotic number of the places of degree r for any r ≥ 1 in E , if those of F are known? We give a method based on explicit extension...
متن کاملGalois Towers over Non-prime Finite Fields
In this paper we construct Galois towers with good asymptotic properties over any nonprime 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/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 ...
متن کاملClassical Wavelet Transforms over Finite Fields
This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 1998
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927879808826370