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Golay complementary set (GCS) plays a vital role in reducing peak-to-meanenvelope power ratio (PMEPR) in orthogonal frequency division multiplexing(OFDM). A more general version of GCS is a multiple shift complementary set(MSCS), where by relaxing the condition of zero auto-correlation sum throughoutall the non-zero time shifts to the integer multiples of some fixed time shift,more sequence sets can be made available. In this paper, we propose directconstructions of MSCSs with flexible and arbitrary lengths and flexible setsizes, by using multivariable functions, which have not been reported before.

Direct Constructions of Multiple Shift Complementary Sets of Flexible Lengths