Extending two families of maximum rank distance codes
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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.
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