A Construction for Constant Dimension Codes from the Known Codes

One of the most fundamental topics in subspace coding is to explore the maximal possible value A(q)(n, d, k) of a set of k-dimensional subspaces in F-q(n) such that the subspace distance satisfies d(S)(U, V) = dim(U + V) - dim(U boolean AND V) >= 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 from the existing results. This construction is done by merging two existing constructions, which exceeds the latest improvements including the cases: A(2)(8, 4, 3) >= 1331 and A(2)(8, 4, 4) >= 4802.