A remark on ${\mathbb{F}}_{q^n}$-Linear MRD codes

Abstract

In this note, we provide a description of the elements of minimum rank of a generalized Gabidulin code in terms of Grassmann coordinates. As a consequence, a characterization of linearized polynomials of rank at most $n-k$ is obtained, as well as parametric equations for MRD-codes of distance $d=n-k+1$.

The results are not relevant enough in light of previous literature

References in corpus (3)

• Generalized Twisted Gabidulin Codes
• On kernels and nuclei of rank metric codes
• Maximum scattered linear sets and MRD-codes