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

2024/01/11 by Smaldore, Valentino, Zanella, Corrado, Zullo, Ferdinando
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2401.06085

Abstract

In this paper we will study the action of \mathbbFqn2 × 2 on the graph of an \mathbbFq-linear function of \mathbbFqn 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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