Construction of Constant Dimension Codes in Some Cases

Abstract

In this paper, we study further bounds of constant dimension codes in Grassmannian space ${\mathcal{G}}_q(n,k)$. There is increasing interest in subspace codes since they are essential for error-correction in networks. Additionally, there is a connection to the theory over finite fields. By revising the specific construction methods of the constant dimension codes in [1], [2], we improve some bounds on $q$-ary constant dimension codes in certain cases.