Generalised Rudin-Shapiro Constructions

A Golay Complementary Sequence (CS) has Peak-to-Average-Power-Ratio (PAPR) ≤ 2.0 for its one-dimensional continuous Discrete Fourier Transform (DFT) spectrum. Davis and Jedwab showed that all known length 2m CS, (GDJ CS), originate from certain quadratic cosets of Reed-Muller (1, m). These can be generated using the Rudin-Shapiro construction. This paper shows that GDJ CS have PAPR ≤ 2.0 under all unitary transforms whose rows are unimodular linear (Linear Unimodular Unitary Transforms (LUUTs)), including one- and multi-dimensional generalised DFTs. We also propose tensor cosets of GDJ sequences arising from Rudin-Shapiro extensions of near-complementary pairs, thereby generating many infinite sequence families with tight low PAPR bounds under LUUTs.