Primitive normal values of rational functions over finite fields

In this paper, we consider rational functions f with some minor restrictions over the finite field Fqn , where q = p for some prime p and positive integer k. We establish a sufficient condition for the existence of a pair (α, f(α)) of primitive normal elements in Fqn over Fq. Moreover, for q = 2 and rational functions f with quadratic numerators and denominators, we explicitly find that there are at most 55 finite fields Fqn in which such a pair (α, f(α)) of primitive normal elements may not exist.

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