New Construction for Constant Dimension Subspace Codes via a Composite Structure

Abstract

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 ${\mathrm{d}}_{\mathrm{S}}(U,V)=\dim (U+V)-\dim (U\cap V)\ge d$ for any two different $k$-dimensional subspaces $U$ and $V$ in this set. In this paper, 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.

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