MRD-codes arising from the trinomial xq+xq3+cxq5∈Fq6[x]

Abstract In [10] , the existence of F q -linear MRD-codes of F q 6 × 6 , with dimension 12, minimum distance 5 and left idealiser isomorphic to F q 6 , defined by a trinomial of F q 6 [ x ] , when q is odd and q ≡ 0 , ± 1 ( mod 5 ) , has been proved. In this paper we show that this family produces F q -linear MRD-codes of F q 6 × 6 , with the same properties, also in the remaining q odd cases, but not in the q even case. These MRD-codes are not equivalent to the previously known MRD-codes. We also prove that the corresponding maximum scattered F q -linear sets of PG ( 1 , q 6 ) are not P Γ L ( 2 , q 6 ) -equivalent to any previously known linear set.