Sequences and their correlation properties have been extensively studied due to their broad applications. In this paper, we develop a connection between sequences and well-studied combinatorial objects, circular Florentine arrays. This connection allows us to derive two types of sequences with good correlation properties. The first type consists of sequences having optimal correlation with respect to the Sarwate bound. Our constructions are based on perfect polyphase sequences. The number of perfect sequences with optimal correlation depends on the existence of circular Florentine arrays, which improves the previous known results. The second type is about multiple ZCZ sequence sets with low inter-set cross-correlation. Each generated ZCZ sequence set is optimal with respect to the Tang-Fan-Matsufuji bound, and each sequence in each set is perfect. In addition, any two sequences from distinct ZCZ sequence sets possess optimal inter-set cross-correlation with respect to the Sarwate bound. Compared with the previous results, the number of ZCZ sequence sets with optimal inter-set cross-correlation property is improved, because of the existence of 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.

Zero correlation zone (ZCZ) sequences are a class of spreading sequences having ideal auto-correlation and cross correlation in a zone around the origin. They have been extensively studied in recent years due to their important applications in quasi-synchronous code division multiple access systems. In this paper, a construction of ZCZ sequence sets is proposed based on perfect nonlinear functions. It generates multiple ZCZ sequence sets with the properties: 1) each sequence is perfect in the sense that its out-of-phase auto-correlation is always zero; 2) each ZCZ sequence set is optimal with respect to the Tang-Fan-Matsufuji bound in which all the sequences are pairwise cyclically distinct; and 3) the maximum inter-set cross correlation of multiple sequence sets achieves the well-known Sarwate bound.