Connections between scattered linear sets and MRD-codes

01/27/2020

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by   Olga Polverino, et al.

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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 PG(1,q^n) define square MRD-codes. Later in "Maximum scattered linear sets and MRD-codes" (2017) maximum scattered linear sets in PG(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 PG(n,q)" (2000).