Construction of Const Dimension Codes from Serval Parallel Lift MRD Code

Abstract

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).