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arXiv · 2002.00500

Exceptional scatteredness in prime degree

Andrea Ferraguti·Giacomo Micheli
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Abstract

Let $q$ be an odd prime power and $n$ be a positive integer. Let $\ell\in \mathbb F_{q^n}[x]$ 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 $\ell=x$. 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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Andrea Ferraguti, Giacomo Micheli. 2020-02-02. Exceptional scatteredness in prime degree. https://arxiv.org/abs/2002.00500

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