Unified construction of perfect polyphase sequences

Polyphase sequences over N-th complex roots of unity are considered. A sequence is perfect if all its out-of-phase periodic autocorrelation equal zero. This paper shows that all previously known perfect polyphase sequences (PPS) constructions, can be classified into four classes: (1) generalized Frank sequences (2) generalized chirp-like polyphase sequences, (3) Milewski sequences, and (4) PPS associated with the general construction of generalized bent function. The key result is a unified construction of PPS which includes these four classes as special cases. Here only explicit constructions of PPS are considered because PPS obtainable by applying appropriate transformations to one or more previously explicitly constructed PPS are always obtainable from the unified construction in the same manner.