A new family of maximum scattered linear sets in PG(1, q6)

We generalize the example of linear set presented by the last two authors in “Vertex properties of maximum scattered linear sets of PG (1,  q n ) " (2019) to a more general family, proving that such linear sets are maximum scattered when q is odd and, apart from a special case, they are new. This solves an open problem posed in “Vertex properties of maximum scattered linear sets of PG (1,  q n ) " (2019). As a consequence of Sheekey’s results in “A new family of linear maximum rank distance codes" (2016), this family yields to new MRD-codes with parameters (6, 6,  q ; 5) .