Construction of Const Dimension Codes from Serval Parallel Lift MRD Code

TL;DR

This paper introduces a generalized construction method for constant-dimension codes using parallel lifted MRD codes, providing new lower bounds and leveraging Delsarte's theorem for rank distribution analysis.

Contribution

The paper extends existing methods by generalizing the use of parallel lifted MRD codes and deriving new bounds for constant-dimension subspace codes.

Findings

New lower bounds for Aq((s+1)k+n,d,k)

Generalized construction from multiple parallel lifted MRD codes

Application of Delsarte theorem for rank distribution analysis

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).