Exceptional scatteredness in prime degree

2020/02/02 by Ferraguti, Andrea, Micheli, Giacomo
#11R45 #11T06 #11T71 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2002.00500

Abstract

Let q be an odd prime power and n be a positive integer. Let ℓ∈ \mathbb F_qⁿ[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 \mathbb F_q.

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