In this paper, a novel architecture of spatial/spectral optical code-division multiple-access (OCDMA) systems using partial modified prime (PMP) codes together with error-correction codes is proposed. Using PMP codes for channel division can completely eliminate multiple-user interference and suppress phase-induced intensity noise due to the zero cross-correlation property in each code group. Moreover, by applying convolutional codes on the spectral slices of output optical signals, the system performance can be further improved without extra bandwidth. Numerical results show that the proposed system can accommodate 147 simultaneous users and the data rate of each user can achieve 10 Gbps at bit error rate around 10-9 and spectral width equal to 30 nm. Compared with other conventional spatial/spectral OCDMA systems, the proposed system has lower complexity and better performance.