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A novel prime code, hereby referred to as 'double- padded modified prime code', is introduced and employed in a coherent optical code-division multiple-access (OCDMA). We have analyzed this system signal-to-noise ratio (SNR) penalty as a function of the number of simultaneous users incurred to maintain an appropriate value of the bit-error rate (BER). As a coherent modulation the binary phase-shift keying (BPSK) is analyzed and finally signals are heterodyne-detected and processed at the receiver end. Also, in the analysis both the receiver noise and multiple access interference (MAI) are investigated.