In this work we present results on the classification of Fqn-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 C=⟨Xqt,F(X),G(X)⟩⊆Ln,q of exceptional type, i.e. such that C is MRD over infinitely many extensions of the base field. These results partially address a conjecture of Bartoli, Zini and Zullo in 2023.
On 3-dimensional MRD codes of type $$\langle X^{q^t},X+\delta X^{q^{2t}},G(X) \rangle $$
Bartoli, Daniele
;Ghiandoni, Francesco
2025
Abstract
In this work we present results on the classification of Fqn-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 C=⟨Xqt,F(X),G(X)⟩⊆Ln,q of exceptional type, i.e. such that C is MRD over infinitely many extensions of the base field. These results partially address a conjecture of Bartoli, Zini and Zullo in 2023.File in questo prodotto:
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