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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.
Ferdinando Zullo (Thu,) studied this question.