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We present a new dynamic spreading code selection technique to obtain low peak-to-average-power ratio (PAPR) of an orthogonal frequency-division multiplexing code-division multiple-access (OFDM-CDMA) system with 4-QAM modulation for the down-link in mobile communication. In this method, initially, each user is assigned a low and a high PAPR spreading code, which allows selecting one when the system is operating. The spreading code of each user is dynamically selected so that total PAPR level of the whole user group present in the system is minimized. With the proposed technique, the PAPR level of a system with 10 users and 64 sub-carriers using 64 chip Walsh-Hadamard (WH) codes, can be limited to 15 dB while the worst case theoretical maximum could go up to 28.1 dB. Although 64 chip WH codes are employed to evaluate the performance it can be generalized to all other sets of spreading codes.