  In this paper, we generalize the method of using two parallel versions of the
lifted MRD code from the existing work [1]. The Delsarte theorem of the rank
distribution of MRD codes is an important part to count codewords in our
construction. We give a new generalize construction to the following bounds: if
n>=k>=d, then $Aq(n +
k,k,d)>=q^{n(k-\frac{d}{2}+1)}+\sum_{r=\frac{d}{2}}^{k-\frac{d}{2}}
A_r(Q_q(n,k,\frac{d}{2})).$ On this basis, we also give a construction of
constant-dimension subspace codes from several parallel versions of lifted MRD
codes. This construction contributes to a new lower bounds for
Aq((s+1)k+n,d,k).
