New Optimal Sets of Perfect Polyphase Sequences Based on Circular Florentine Arrays

Families of periodic sequences with some desirable auto-correlation and cross-correlation properties have applications in communications and radar systems for identification, synchronization, ranging, or interference mitigation. A sequence is said to be a polyphase sequence if all the coordinates are n-th roots of unity. In this paper, we develop a connection between generalised Frank sequences and well-studied combinatorial objects: circular Florentine arrays. From this connection, we can derive an optimal set of perfect polyphase sequences with respect to the Sarvate bound. Furthermore, the size of the optimal set is determined by the existence of circular Florentine arrays. As a result, the size of an optimal set of perfect sequences is increased, compared with the previous results, where the size depends on the smallest prime divisor of the period.