Golay complementary set (GCS) plays a vital role in reducing peak-to-mean envelope 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 throughout all 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 direct constructions of MSCSs with flexible and arbitrary lengths and flexible set sizes, by using multivariable functions, which have not been reported before.

翻译：戈莱互补集在正交频分复用中降低峰值均值包络功率比方面发挥着重要作用。多移位互补集是戈莱互补集的一种更广义形式，通过将非零时移处的零自相关和条件放宽到某个固定时移的整数倍，可以生成更多的序列集。本文提出了一种利用多元函数直接构造具有灵活任意长度和灵活集合规模的多移位互补集的方法，这一成果此前未见报道。