New Construction of Complementary Sequence (or Array) Sets and Complete Complementary Codes

A new method to construct $q$ -ary complementary sequence sets (CSSs) and complete codes (CCCs) of size $N$ is proposed by using desired para-unitary (PU) matrices. The concept seed PU matrices introduced a systematic approach on how compute the explicit forms functions in constructed CSSs CCCs from given. general form these only depends basis ${\mathbb Z}_{N}$ Z}_{q}$ representatives equivalent class Butson-type Hadamard (BH) Especially, realization Golay pairs our exactly coincides with standard pairs. ternary sequences 3 first reported here. For quaternary 4, almost all derived here are never before. Generalized recursive constructions also studied, large number given accordingly. From perspective this paper, known results GBF literature (except non-standard pairs) WHT This suggests that other BH will yield significantly increasing low peak-to-mean envelope power ratio.