A New Construction of Golay Complementary Sets of Non-Power-of-Two Length Based on Boolean Functions

Golay complementary sets have found many applications in communications, e.g., they have been proposed to control the high peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals. The relationship between Golay complementary sets and generalized Reed-Muller codes have been proposed to construct Golay complementary sets of length $2^m$ based on generalized Boolean functions. However, the number of used subcarriers is usually non-power-of-two in practical wireless OFDM-based communication systems. In this paper, a new construction of Golay complementary sets of length not equal to $2^m$ based on generalized Boolean functions is proposed. The constructed Golay complementary sets exist for various lengths not equal to $2^m$ and have PAPRs upper bounded by the set size.

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