New Construction for Constant Dimension Subspace Codes via a Composite Structure

One of the most fundamental topics in subspace coding is to explore the maximal possible value ${\mathbf{A}}_{q}(n,d,k)$ of a set of $k$ -dimensional subspaces in $\mathbb F_{q}^{n}$ such that the subspace distance satisfies $\text {d}_{\text {S}}(U,V) = \dim (U+V)-\dim (U\cap V)\,\,\geq d$ for any two different $k$ -dimensional subspaces $U$ and $V$ in this set. In this letter, we propose a construction for constant dimension subspace codes by inserting a composite structure composing of an MRD code and its sub-codes. Its vast advantage over the previous constructions has been confirmed through extensive examples. At least 49 new constant dimension subspace codes which exceeds the currently best codes are constructed.