Improved generalized block inserting construction of constant dimension codes

Constant dimension codes (CDCs) have received extensive attention due to their applications in random network coding. The basic problem for CDCs is to determine the maximal possible cardinality Aq(n,d,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A_q(n,d,k)$$\end{document} of CDC for given parameters q, n, d and k. In this paper, we present some variations on the generalized block inserting construction method. These constructions insert more subspaces into the CDC from the parallel linkage construction via changing the parameters and shifting the positions of some small matrices. Our constructions help us to obtain CDCs with larger cardinalities and some new lower bounds for CDCs which are better than the previously best known ones.