On the stabilizer of the graph of linear functions over finite fields
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910294733750272 |
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| author | Smaldore, Valentino Zanella, Corrado Zullo, Ferdinando |
| author_facet | Smaldore, Valentino Zanella, Corrado Zullo, Ferdinando |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the stabilizer of the graph of linear functions over finite fields Smaldore, Valentino Zanella, Corrado Zullo, Ferdinando Combinatorics Information Theory 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. |
| title | On the stabilizer of the graph of linear functions over finite fields |
| topic | Combinatorics Information Theory |
| url | https://arxiv.org/abs/2401.06085 |