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We show that a constant amplitude multi-code (CAMC) CDMA in a recursive structure can be reconfigured into a single parity check, product code (SPCPC). CAMC can benefit from error correction by parity decoding. We present an algorithm which reconfigures CAMC into an SPCPC structure and then refines the log likelihood ratio of the received bits in an iterative way. Computer simulation results show that CAMC has a superior performance of error correction than a generic SPCPC. Hence, CAMC provides both a low PAPR and robustness to bit errors.