Connections between scattered linear sets and MRD-codes

The aim of this paper is to survey on the known results on maximum scattered linear sets and MRD-codes. In particular, we investigate the link between these two areas. In “A new family of linear maximum rank distance codes” (2016) Sheekey showed how maximum scattered linear sets of $\mathrm{P}\mathrm{G}(1,q^n)$ define square MRD-codes. Later in “Maximum scattered linear sets and MRD-codes” (2017) maximum scattered linear sets in $\mathrm{P}\mathrm{G}(r-1,q^n)$, $r>2$, were used to construct non square MRD-codes. Here, we point out a new relation regarding the other direction. We also provide an alternative proof of the well-known Blokhuis-Lavrauw’s bound for the rank of maximum scattered linear sets shown in “Scattered spaces with respect to a spread in $\mathrm{P}\mathrm{G}(n,q)$” (2000).