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MiS Preprint

Extending two families of maximum rank distance codes

Alessandro Neri, Paolo Santonastaso and Ferdinando Zullo


In this paper we provide a large family of rank-metric codes, which contains properly the codes recently found by Longobardi and Zanella (2021) and by Longobardi, Marino, Trombetti and Zhou (2021). These codes are $\mathbb{F}_{q^{2t}}$-linear of dimension $2$ in the space of linearized polynomials over $\mathbb{F}_{q^{2t}}$, where $t$ is any integer greater than $2$, and we prove that they are maximum rank distance codes. For $t\ge 5$, we determine their equivalence classes and these codes turn out to be inequivalent to any other construction known so far, and hence they are really new.

Jun 8, 2021
Jun 8, 2021
MSC Codes:
11T71, 11T06, 94B05
rank-metric codes, linearized polynomials, MRD codes, scattered polynomials

Related publications

2022 Repository Open Access
Alessandro Neri, Paolo Santonastao and Ferdinando Zullo

Extending two families of maximum rank distance codes

In: Finite fields and their applications, 81 (2022), p. 102045