Two-Valued Periodic Complementary Sequences

摘要

We present a novel transform for periodic complementary sets (PCSs) over two-valued alphabets from a large set of difference families. This is achieved by generalizing Golomb's idea in 1992, which was for transformed perfect sequences with zero autocorrelations only. Based on the properties of difference family, a sufficient condition for such two-valued PCSs is derived. Systematic constructions of two-valued periodic complementary pairs are presented. It is shown that many lengths for which binary PCSs do not exist become admissible for our proposed two-valued PCSs.