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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.

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