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In this paper, we show the equivalence between complementary code keying (CCK) codeword and coset of the first order Reed-Muller (RM) code with variables of three. The CCK codewords are Golay sequences which have peak-to-average power ratio (PAPR) of two at most and can correct one error. We propose a CCK-orthogonal frequency division multiplexing (OFDM) modem to reduce PAPR. Also, we present the performance improvement techniques by increasing the variables of four to correct three errors and reduce PAPR at least 9dB with this system. Although, two Fast Hadamard Transform (FHT) blocks of size 8 × 64 are required at the receiver, we reduce the complexity by using FHT blocks of size 8 × 64 and 2 × 4 without deteriorating the performance. We generalize our results that we may increase the variables of RM code to enhance the error correcting and PAPR reduction capabilities without increasing receiver's complexity.