Several constructions of constant dimension code using equal-division method

Constant dimension codes (CDCs) have garnered significant attention in recent years, primarily owing to their crucial applications in random network coding. A central problem in the study of CDCs involves determining the maximum achievable cardinality, denoted as $A_q(n,2\delta ,k)$ for given parameters. In this paper, we propose a new approach to constructing CDCs based on the equal-division method, which we subsequently combine with existing optimal codes from prior literature. The resulting codes yield improved lower bounds for $A_q(n,2\delta ,k)$ compared to previously established results across certain parameters. Furthermore, we extend our approach by incorporating multiple constructions based on distinct ways of equal division. The newly constructed CDCs have larger cardinality under some parameters.