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 [57] Sheekey showed how maximum scattered linear sets of PG(1,qn) define square MRD-codes. Later in [13] maximum scattered linear sets in PG(r - 1, qn), 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 [6].
Connections between scattered linear sets and MRD-codes
Polverino O.;Zullo F.
2020
Abstract
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 [57] Sheekey showed how maximum scattered linear sets of PG(1,qn) define square MRD-codes. Later in [13] maximum scattered linear sets in PG(r - 1, qn), 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 [6].File in questo prodotto:
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