Extending two families of maximum rank distance codes

Alessandro Neri, Paolo Santonastaso, and Ferdinando Zullo

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Submission date: 08. Jun. 2021
Bibtex
MSC-Numbers: 11T71, 11T06, 94B05
Keywords and phrases: rank-metric codes, linearized polynomials, MRD codes, scattered polynomials
Link to arXiv: See the arXiv entry of this preprint.

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 𝔽_q^2t-linear of dimension 2 in the space of linearized polynomials over 𝔽_q^2t, where t is any integer greater than 2, and we prove that they are maximum rank distance codes. For t ≥ 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.