We have introduced a flexible OFDM structure based on a promising property of IFFT operation. This structure can support uplink applications which include many transmitters using different numbers of subcarriers and one receiver with just one IFFT/FFT module with the subcarriers of the least common multiple (LCM) for the number of subcarriers of all the transmitters. In this paper, combining the parallel combinatory (PC) code and the proposed flexible OFDM structure, we report the design of a new OFDM system with PC code for various applications with a moderate transmission rate. The system can select appropriate phase sets for all modulated subcarriers for each PC code for different design requirements such as peak-to-average power ratio (PAPR) reduction or BER performance improvement. The proposed system will achieve better PAPR characteristics and promising BER performance. In addition, due to the flexible OFDM structure, the proposed PC-OFDM system will also have properties of high adaptability and compatibility.