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Selected mapping (SLM) schemes are commonly employed to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. It has been shown that the computational complexity of the traditional SLM scheme can be substantially reduced by adopting conversion vectors obtained by using the inverse fast Fourier transform (IFFT) of the phase rotation vectors in place of the conventional IFFT operations [C.-L. Wang and Y. Ouyang, ??Low-Complexity Selected Mapping Schemes for Peak-to-Average Power Ratio Reduction in OFDM Systems,?? IEEE Trans. Signal Process., vol. 53, no. 12, pp. 4652-4660, Dec. 2005]. To ensure that the elements of these phase rotation vectors have an equal magnitude, conversion vectors should have the form of a perfect sequence. This paper presents three novel classes of perfect sequence, each of which comprises certain base vectors and their cyclically shifted versions. Three novel low-complexity SLM schemes are then proposed based upon the unique structures of these perfect sequences. It is shown that while the PAPR reduction performances of the proposed schemes are marginally poorer than that of the traditional SLM scheme, the three schemes achieve a substantially lower computational complexity.