A novel type of optical spreading sequences, named the 'new-Modified Prime Code (nMPC)', is proposed for use in synchronous direct-detection optical code-division multiple-access (CDMA) systems which employ both pulse position modulation (PPM) and overlapping pulse position modulation (OPPM) schemes. The upper bounds on the bit error rate (BER) for nMPC used in PPM-CDMA systems are derived and compared with the respective systems, using a modified prime code (MPC) and a padded modified prime code (PMPC). The nMPC is further applied to the OPPM-CDMA system and the system with a proposed interference cancellation scheme. Our results show that under the same conditions the PPM-CDMA system performances are more improved with the use of nMPC than with the two other traditional codes. Moreover, they show that the system performances are significantly enhanced by the proposed interference reduction methods, if the nMPC is used in the OPPM-CDMA systems.