A note on the distribution of self-dual normal bases generators of finite fields under trace map
نویسنده
چکیده
Let Fqn be an extension of the field Fq of degree n = mpl , l ≥ 1 where p is the characteristic of the field Fq . It is proved that the number of self-dual normal bases generators of Fqn over Fq in (TrFqn |Fqm ) −1(β), for any self-dual normal basis generator β of Fqm over Fq , is independent of the choice of β.
منابع مشابه
Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields
Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that TrF/E(g(x), h(x)) = δg,h for g, h ∈ Γ. Bayer-Fluckiger and Lenstra have shown that when char(E) 6= 2, then F admits a self-dual normal basis if and only if [F : E] is odd. If F/E is an extension of finite fields and char(E) = 2, then F ...
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