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}.