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This paper proposes a novel evolutionary approach to spreading code design in direct sequence code division multiple access (DS-CDMA). Specifically, a multiobjective evolutionary algorithm (EA) is used to generate complex spreading sequences that are optimized with respect to the average mean-square cross- and/or autocorrelation (CC and/or AC) properties. A theoretical model is developed in order to demonstrate the optimality of the generated codes. The proposed algorithm enables spreading code design with no constraints on the code length. Furthermore, it is possible to generate K≥N codes of length N with very little cost in correlation properties. This results in significant capacity enhancement in DS-CDMA systems.