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Spectrally encoded (SE) CDMA systems, a. k. a. spread time (ST) CDMA systems, have several advantages over their frequency-time dual, direct-sequence CDMA such as the abilities to shape the transmitted spectrum and to avoid narrow-band interference. However, no orthogonal spreading code has been proposed to efficiently avoid multiple-access interference (MAI). In this paper, we propose a novel orthogonal spreading code for SE-CDMA. We study undesirable channel conditions under which the orthogonality property of the code could be lost. We propose a chip normalizing scheme (CNS) to restore the orthogonality property of the code in these cases. Our simulation results show that the encoded system can achieve the performance of interference-free channels. Furthermore, using our CNS the users can achieve a higher bit rate at the same bit error rate as the unnormalized case.