New Construction for Constant Dimension Subspace Codes via a Composite Structure
Xianmang He, Yindong Chen, Zusheng Zhang, Kunxiao Zhou · IEEE Communications Letters · 2021
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.