On $3$-dimensional MRD codes of type $\langle x^{q^t},x+δx^{q^{2t}},G(x) \rangle$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910352997875712 |
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| author | Bartoli, Daniele Ghiandoni, Francesco |
| author_facet | Bartoli, Daniele Ghiandoni, Francesco |
| contents | In this work we present results on the classification of $\mathbb{F}_{q^n}$-linear MRD codes of dimension three. In particular, using connections with certain algebraic varieties over finite fields, we provide non-existence results for MRD codes $\mathcal{C}=\langle x^{q^t}, F(x), G(x) \rangle \subseteq \mathcal{L}_{n,q}$ of exceptional type, i.e. such that $\mathcal{C}$ is MRD over infinite many extensions of the field $\mathbb{F}_{q^n}$. These results partially address a conjecture of Bartoli, Zini and Zullo in 2023. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $3$-dimensional MRD codes of type $\langle x^{q^t},x+δx^{q^{2t}},G(x) \rangle$ Bartoli, Daniele Ghiandoni, Francesco Information Theory Algebraic Geometry In this work we present results on the classification of $\mathbb{F}_{q^n}$-linear MRD codes of dimension three. In particular, using connections with certain algebraic varieties over finite fields, we provide non-existence results for MRD codes $\mathcal{C}=\langle x^{q^t}, F(x), G(x) \rangle \subseteq \mathcal{L}_{n,q}$ of exceptional type, i.e. such that $\mathcal{C}$ is MRD over infinite many extensions of the field $\mathbb{F}_{q^n}$. These results partially address a conjecture of Bartoli, Zini and Zullo in 2023. |
| title | On $3$-dimensional MRD codes of type $\langle x^{q^t},x+δx^{q^{2t}},G(x) \rangle$ |
| topic | Information Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2403.01887 |