Fault detection (FD) of networked control systems (NCS) with limited communication is addressed in this article. In periodic communication sequence-based NCS, at each time instant only parts of the actuators and sensors are allowed to communicate with the central FD system, which leads to incomplete plant information at the central station. In this article, a parity space based multi-solution FD scheme is proposed based on different information structures of the incomplete plant information. In this multi-solution scheme, each solution is an independent residual generator and has different properties. It is proved that there is a tradeoff between fast FD and detection performance, i.e. the solution with a smaller FD delay has a poorer fault sensitivity and thus a larger miss detection rate, whereas the one with a higher fault sensitivity has a larger FD delay. The FD scheme can be realised by diagnostic observers as well, which have more design freedom. Simulation results are also given to illustrate the results obtained.