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 <inline-formula> <tex-math notation="LaTeX">${\mathbf{A}}_{q}(n,d,k)$ </tex-math></inline-formula> of a set of <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-dimensional subspaces in <inline-formula> <tex-math notation="LaTeX">$\mathbb F_{q}^{n}$ </tex-math></inline-formula> such that the subspace distance satisfies <inline-formula> <tex-math notation="LaTeX">$\text {d}_{\text {S}}(U,V) = \dim (U+V)-\dim (U\cap V)\,\,\geq d$ </tex-math></inline-formula> for any two different <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-dimensional subspaces <inline-formula> <tex-math notation="LaTeX">$U$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula> 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.

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