MRD-codes arising from the trinomial x^q+x^q^3+cx^q^5∈F_q^6[x]
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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 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 PΓL(2,q^6)-equivalent to any previously known scattered linear set.
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