Polyphase sequences with good correlation properties

Design of sequences with good auto and crosscorrelation properties is one of the main tasks in several applications, including multi-user radar, sonar, and communications. In this paper we describe a new construction of polyphase sequences with optimal correlation properties. The construction includes, as special cases, a family of finite chirps and two previously proposed families of communications sequences. The main tool used in the construction is the finite Zak transform. The construction suggests several further generalizations that can be obtained by operating exclusively on subgroups of the permutation group.