Constructions and a generalization of perfect autocorrelation sequences on Z

Low autocorrelation signals have fundamental applications in radar and communications. We construct constant amplitude zero autocorrelation (CAZAC) sequences x on the integers Z by means of Hadamard matrices. We then generalize this approach to construct unimodular sequences x on Z whose autocorrelations Ax are building blocks for all functions on Z. As such, algebraic relations between Ax and Ay become relevant. We provide conditions for the validity of the formulas Ax+y = Ax +Ay.