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A new scheme for peak-to-average power ratio reduction in OFDM systems is proposed. Reed-Solomon codes are employed to create a number of candidates, from which the best are selected. Thereby, in contrast to existing approaches, the codes are arranged over a number of OFDM frames rather than over the carriers. The performance of the new scheme is shown for two examples: multi-antenna systems and packet transmission. Significant gains can be achieved with this very flexible and versatile method.