New Framework for Sequences With Perfect Autocorrelation and Optimal Crosscorrelation.

In this paper, we give a new framework for constructing perfect sequences, called generalized Milewski sequences, over various alphabets including Polyphase (PSK) as well as Amplitude-and-Polyphase (APSK) in general, and for constructing optimal sets of such perfect sequences by using combinatorial designs, called circular Florentine arrays. Specifically, we prove that, given any positive integer $m\geq 1$ , (i) there exists a perfect sequence of period $mN^{2}$ for any positive integer $N$ if there exists a perfect sequence (polyphase or not) of length $m$ ; (ii) an optimal $k$ -set of perfect sequences of length $mN^{2}$ can be constructed if there exist both a $k \times N$ circular Florentine array and an optimal $k$ -set of perfect sequences all of length $m$. This enables us to find some optimal $k$ -set of perfect sequences where $k > p_{\text {min}}-1$ , where $p_{\text {min}}$ is the smallest prime factor of $mN^{2}$. [ABSTRACT FROM AUTHOR]