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On $3$-dimensional MRD codes of type $\langle x^{q^t},x+δ x^{q^{2t}},G(x) \rangle$ (2403.01887v1)

Published 4 Mar 2024 in cs.IT, math.AG, and math.IT

Abstract: In this work we present results on the classification of $\mathbb{F}{qn}$-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 $\mathcal{C}=\langle x{qt}, F(x), G(x) \rangle \subseteq \mathcal{L}{n,q}$ of exceptional type, i.e. such that $\mathcal{C}$ is MRD over infinite many extensions of the field $\mathbb{F}_{qn}$. These results partially address a conjecture of Bartoli, Zini and Zullo in 2023.

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