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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
15/2021

Extending two families of maximum rank distance codes

Alessandro Neri, Paolo Santonastaso and Ferdinando Zullo

Abstract

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.

Received:
08.06.21
Published:
08.06.21
MSC Codes:
11T71, 11T06, 94B05
Keywords:
rank-metric codes, linearized polynomials, MRD codes, scattered polynomials

Related publications

inJournal
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