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In this paper, we have proposed a novel spreading code-set based on the prime code families, hereby referred to as transposed sparse-padded modified prime code for synchronous optical code-division multiple-access (OCDMA) networks. The proposed code-set is compared with modified prime codes (MPCs) in terms of correlation properties, bit-error rate (BER), and cardinality. This new low-weight large code-set has better correlation characteristics as compared with MPC families and, as results indicated, the new code-set has considerably improved the BER and power consumption of the OCDMA networks. We have analyzed the performance of the proposed code-set in both incoherent ON-OFF keying and pulse position modulation OCDMA systems, while the multiple access interference was the major degrading quality. The results indicate that at the BER floor of 10-9, the proposed code-set can accommodate greater number of users and consume less power as compared with the MPC under the same transmission conditions.