Saturating linear sets in PG(2,q⁴)

Bonini, Borello and Byrne started the study of saturating linear sets in Desarguesian projective spaces, in connection with the covering problem in the rank metric. In this paper we study $1$-saturating linear sets in PG(2,q⁴), that is Fq-linear sets in PG(2,q⁴) with the property that their secant lines cover the entire plane. By making use of a characterization of generalized Gabidulin codes, we prove that the rank of such a linear set is at least $5$. This answers to a recent question posed by Bartoli, Borello and Marino.