On 3-dimensional MRD codes of type ⟨ x^qt,x+δx^q^2t,G(x) ⟩

2024/03/04 by Daniele Bartoli, Bartoli, Daniele, Francesco Ghiandoni +1
Computer Science · Engineering · #Algebraic Geometry (math.AG) #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2403.01887

openalex publication_date 2024/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we present results on the classification of \mathbbF_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 C=⟨ x^qt, F(x), G(x) ⟩ ⊆ L_n,q of exceptional type, i.e. such that C is MRD over infinite many extensions of the field \mathbbF_qⁿ. These results partially address a conjecture of Bartoli, Zini and Zullo in 2023.

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