TY - JOUR
T1 - MRD-codes arising from the trinomial xq+xq3 +cxq5 ∈Fq6 [x]
AU - Marino, Giuseppe
AU - Montanucci, Maria
AU - Zullo, Ferdinando
PY - 2020/4/15
Y1 - 2020/4/15
N2 - In [10], the existence of Fq-linear MRD-codes of Fq 6×6, with dimension 12, minimum distance 5 and left idealiser isomorphic to Fq6 , defined by a trinomial of Fq6 [x], when q is odd and q≡0,±1(mod5), has been proved. In this paper we show that this family produces Fq-linear MRD-codes of Fq 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 Fq-linear sets of PG(1,q6) are not PΓL(2,q6)-equivalent to any previously known linear set.
AB - In [10], the existence of Fq-linear MRD-codes of Fq 6×6, with dimension 12, minimum distance 5 and left idealiser isomorphic to Fq6 , defined by a trinomial of Fq6 [x], when q is odd and q≡0,±1(mod5), has been proved. In this paper we show that this family produces Fq-linear MRD-codes of Fq 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 Fq-linear sets of PG(1,q6) are not PΓL(2,q6)-equivalent to any previously known linear set.
KW - Linear set
KW - MRD-code
KW - Scattered subspace
U2 - 10.1016/j.laa.2020.01.004
DO - 10.1016/j.laa.2020.01.004
M3 - Journal article
AN - SCOPUS:85077733099
SN - 0024-3795
VL - 591
SP - 99
EP - 114
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -