High PAPR (peak to average power ratio) happens because of the summation of Walsh codes in the multicode CDMA (code division multiple access) communication system. In this paper, we propose a binary CA-MC-CDMA (constant amplitude multicode code division multiple access) system to solve the high PAPR problem. Unlike the conventional pre-coding method, there is no loss of bandwidth efficiency in the proposed system because the code rate is always I. The proposed system always generates output signal with 0 db PAPR. The proposed binary CA-MC-CDMA system is based on the 2/2 and 4/4 binary CA-MC-CDMA systems. The proposed system can be easily extended into a large number of parallel multi-code branches by multiple combinations of these two systems. From the computer simulation results, it can be seen that the proposed binary CA-MC-CDMA system always produces binary constant amplitude output data without any loss of code rate, which cannot be found in the conventional MC-CDMA using a pre-coding method. Therefore, it can prevent the nonlinear distortion in the HPA and maximization of HPA power efficiency can be available in the data transmission using multi-code.