Exceptional scatteredness in prime degree

02/02/2020

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by   Andrea Ferraguti, et al.

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Let q be an odd prime power and n be a positive integer. Let ℓ∈F_q^n[x] be a q-linearised t-scattered polynomial of linearized degree r. Let d=max{t,r} be an odd prime number. In this paper we show that under these assumptions it follows that ℓ=x. Our technique involves a Galois theoretical characterization of t-scattered polynomials combined with the classification of transitive subgroups of the general linear group over the finite field F_q.