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arXiv · 2401.06085

On the stabilizer of the graph of linear functions over finite fields

Valentino Smaldore·Corrado Zanella·Ferdinando Zullo
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Abstract

In this paper we will study the action of $\mathbb{F}_{q^n}^{2 \times 2}$ on the graph of an $\mathbb{F}_q$-linear function of $\mathbb{F}_{q^n}$ into itself. In particular we will see that, under certain combinatorial assumptions, its stabilizer (together with the sum and product of matrices) is a field. We will also see some examples for which this does not happen. Moreover, we will establish a connection between such a stabilizer and the right idealizer of the rank-metric code defined by the linear function and give some structural results in the case in which the polynomials are partially scattered.

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Valentino Smaldore, Corrado Zanella, Ferdinando Zullo. 2024-01-11. On the stabilizer of the graph of linear functions over finite fields. https://arxiv.org/abs/2401.06085

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