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Aiming at a single-source multicast network, this paper studies the intrinsic mechanism of linear network coding and proposes a technique of generation and extension between two coding schemes at different multicast rates. The coding scheme is a generation of some coding schemes at higher multicast rate, and it is also an extension of some coding schemes at lower multicast rates. Furthermore, the determinate relationship among channels' global encoding vectors under two generation-extension coding schemes is discovered. By adopting random network coding, several important properties are derived, which are some of the application values and are helpful in implementing a single-source multicast connection with linear network coding. Several related applications are listed. In particular, this paper highlight a way to improve the throughput of single-source multicast network in dynamic environment and presents a random network coding approach based on retransmission and variable multicast rate, under the condition that each sink node has a feedback path to the source node. Compared with random network coding, this approach is a better way of improving the throughput of network. Simulation experiments of the listed applications have been done, and the results validate the conclusions derived from theoretical analyses.