A central problem in constant dimension code (CDC) research involves determining the maximum achievable size \(A_q(n,2d,k)\) . In this paper, we propose an improved parallel linkage construction of CDCs via the mixed dimension method. By combining mixed dimension subspace codes with generator matrix column transformations, our construction yields more flexible and efficient code designs, leading to enhanced lower bounds on \(A_q(n,2d,k)\) for certain parameter ranges. The resulting codes outperform many previously known constructions, which verifies the effectiveness of the proposed approach.
