Extending two families of maximum rank distance codes

Abstract

In this paper, we properly extend the family of rank-metric codes recently found by Longobardi and Zanella (2021) and by Longobardi, Marino, Trombetti and Zhou (2021). These codes are Fq2t-linear of dimension 2 in the space of linearized polynomials over Fq2t, 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.