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This paper is concerned with a new method to enhance the bandwidth efficiency of an MC-CDMA system by using a residue number based representation for information symbols. The residues are mapped into a set of orthogonal sequences and are transmitted in parallel. A multicarrier modulation scheme is used for both transmission and reception of residue channels. Appropriate error correction methods are employed for enhancing the performance of the system. The aim of this paper is to discuss the issues involved in the design of an RNS based MC-CDMA system and to evaluate the performance of the system in a frequency selective Rayleigh fading channel.