Orthogonal frequency division multiplexing (OFDM) has been widely used in multi-carrier communication systems. However, high the peak-to-average power ratio (PAPR) is a very troublesome problem in OFDM system. In the paper, we propose a construction of Golay complementary sets (GCSs) with size 4 of flexible lengths using even-shift complementary pairs (ESCPs). Based on computer search, we find that there exist a large number of even-shift complementary pairs of various lengths, and we also propose some constructions of ESCPs, which are very useful for the construction of GCSs. INDEX TERMS Orthogonal frequency division multiplexing (OFDM), peak-to-average power ratio (PAPR), even-shift complementary pairs, Golay complementary sets.
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