Let q be an odd prime power and n an integer. Let ℓ∈Fqjavax.xml.bind.JAXBElement@70cefefb[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.

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, Andrea;
2020

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.
Settore MAT/03 - Geometria
Chebotarev density theorem; Exceptionality; Finite fields; Galois theory; Rank metric codes; Scattered linear sets; Scattered polynomials
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/101130
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