MRD-codes and linear sets

In this paper we point out the relationship between linear MRD-codes and various geometric objects as linearized polynomials, linear sets of PG(n−1,qn), and generalized Segre varieties. We introduce and characterize a class of particular linear MRD-codes called Fqn-linear codes with distance n−k+1 proving that such codes are equivalent to (n−k+1)-embeddings of a canonical subgeometry.