New maximum scattered linear sets of the projective line

In [2] and [18] are presented the first two families of maximum scattered Fq-linear sets of the projective line PG(1,qn). More recently in [22] and in [5], new examples of maximum scattered Fq-subspaces of V(2,qn) have been constructed, but the equivalence problem of the corresponding linear sets is left open. Here we show that the Fq-linear sets presented in [22] and in [5], for n=6,8, are new. Also, for q odd, q≡±1,0(mod5), we present new examples of maximum scattered Fq-linear sets in PG(1,q6), arising from trinomial polynomials, which define new Fq-linear MRD-codes of Fq6×6 with dimension 12, minimum distance 5 and left idealiser isomorphic to Fqjavax.xml.bind.JAXBElement@52ca3f68.