A Direct Method to Construct Golay Complementary Sets Based on Boolean Functions

Golay complementary sequences were well studied by Boolean-function generator. Recently, Wang et. al. proposed a new paraunitary-matrix-based construction to generate polyphase Golay complementary sets, in which produces a large number of new Golay complementary set not reported by Boolean-function generator. However, the relationship between the Boolean-function-based construction and paraunitary-matrix-based construction is still unknown. In this paper, we bridge the sequences constructed by these two methods. Moreover, explicit Boolean representations of Golay complementary sets constructed in Wang et. al. are derived by the summation of the Boolean functions which is determined by Hadamard matrix involved in the paraunitary-matrix-based construction.