In wireless communication field, the omnidirectional radiation of electromagnetic wave in free space is always considered as a big shortcoming, nevertheless, it can be used to improve the performace of wireless communication system in network entironment. Here, we consider that M nodes use a switch node to exchang their information in a wireless network. Differert from the conventional method, the switch node will take the joint coding method for the M independent information, then transmit the same codeword to all M nodes simultaneously through the omnidirectional radiation. For the novel network code, the mathematical definition of the M -dimension space-time error correction code is proposed, and some theorems about its performance are proved to lay a foundation to construct good codebooks. The redundancy of time and space domain is added to the novel codebook at the same time, and the efficiency of the transmit power is improved, so we can design high-rate codebook with good error detection and correction capability. Moreover, the complexity of its decoding algorithm can be reduced, owing to the distributed data processing. Here, we emphasize that contrary to one’s intuition, our proposed codebook reveals that it is in general not correct to take the rate of codebook which has the error detection and correction capability to be less than 1.