  As a strategy to further reduce the transmission pressure during the peak
traffic times in wireless network, coded caching has been widely studied
recently. And several coded caching schemes are constructed focusing on the two
core problems in practice, i.e., the rate transmitted during the peak traffic
times and the packet number of each file divided during the off peak traffic
times. It is well known that there exits a tradeoff between the rate and the
packet number. In this paper, a novel recursive construction is proposed. As an
application, several new schemes are obtained. Comparing with previously known
schemes, new schemes could further reduce packet number by increasing little
rate. And for some parameters in coded caching systems, the packet number of
our new schemes are smaller than that of schemes generated by memory sharing
method which is widely used in the field of caching. By the way our new schemes
include all the results constructed by Tang et al., (IEEE ISIT, 2790-2794,
2017) as special cases.
