Summary: By means of the compressed sensing theory under no noise condition, this paper conducts a study on the decoding method of the BCH code. The check matrix is used as the measurement matrices, and the syndrome is used as the measurement signal. Hence, the compressed sensing model of the reconstructing error pattern is built. By the basis pursuit BP algorithm, the error pattern of the BCH code is reconstructed. Taking the (15, 11) BCH code as an example, we have proved that the reconstructing error pattern is correct. According to the receiving code and the reconstructing error pattern, the value of the code word is calculated. On the basis of bit error rate and the code word estimating success rate, the decoding effects of the basis pursuit BP algorithm and the Berlekamp iterative decoding algorithm are analyzed and compared. Taking the BCH short-code and long-code as an example, the simulation experiment is completed. The experiment results prove that the compressed sensing theory and the basis pursuit BP algorithm are feasible and effective in decoding the BCH code.