Construction of Const Dimension Codes from Serval Parallel Lift MRD Code

11/01/2019

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by   Xianmang He, et al.

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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-d/2+1)+∑_r=d/2^k-d/2 A_r(Q_q(n,k,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).