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 Fqjavax.xml.bind.JAXBElement@5067231d-linear of dimension 2 in the space of linearized polynomials over Fqjavax.xml.bind.JAXBElement@26e44682, 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.
Extending two families of maximum rank distance codes
Santonastaso P.;Zullo F.
2022
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 Fqjavax.xml.bind.JAXBElement@5067231d-linear of dimension 2 in the space of linearized polynomials over Fqjavax.xml.bind.JAXBElement@26e44682, 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.File in questo prodotto:
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