On $3$-dimensional MRD codes of type $\langle x^q^t,x+\delta x^q^2t,G(x) \rangle$
<|reference_start|>On $3$-dimensional MRD codes of type $\langle x^q^t,x+\delta x^q^2t,G(x) \rangle$: 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.<|reference_end|>
@article{bartoli2024on,
    title={On $3$-dimensional MRD codes of type $\langle x^{q^t},x+\delta
  x^{q^{2t}},G(x) \rangle$},
    author={Daniele Bartoli and Francesco Ghiandoni},
    journal={arXiv preprint arXiv:2403.01887},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.01887},
    primaryClass={cs.IT math.AG math.IT}
}