Subspace code constructions

Abstract: We improve on the lower bound of the maximum number of planes of ${\rm PG}(8,q)$ mutually intersecting in at most one point leading to the following lower bound: $${\cal A}_q(9, 4; 3) \ge q<sup>{12}+2q<sup>8+2q<sup>7+q<sup>6+q<sup>5+q<sup>4+1$$ for constant dimension subspace codes. We also construct two new non-equivalent $(6, (q^{3-1)(q^2+q+1),} 4; 3)_q$ constant dimension subspace orbit-codes.