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In this paper, we propose a family of newly constructed codes to suppress the phase-induced intensity noise (PIIN) in spectral amplitude-coding (SAC) optical code division multiple access (OCDMA) systems. These new codes are derived from modified prime codes and their cross-correlation is not larger than one. We also present a novel SAC-OCDMA system employing the new codes together with Mach-Zehnder interferometers to eliminate the multi-user interference (MUI). Compared with the systems employing modified quadratic congruence codes (MQC codes), numerical results verify that our proposed system can more effectively suppress the PIIN and eliminate MUI. Hence, the number of simultaneously users and total transmission rate increases significantly.