Let q be an odd prime power and n an integer. Let ℓ∈Fqjavax.xml.bind.JAXBElement@3f28d4ca[x] be a q-linearized 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 Fq.
Exceptional scatteredness in prime degree
Ferraguti A.;
2021-01-01
Abstract
Let q be an odd prime power and n an integer. Let ℓ∈Fqjavax.xml.bind.JAXBElement@3f28d4ca[x] be a q-linearized 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 Fq.
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