Research On New Construction Method Of Difference Set Pairs And Quaternary Sequence Pairs

Because the perfect discrete signal has good autocorrelation properties, it has been applied in many areas such as radar, sonar, modern communication and so on. A lot of construction methods of the perfect discrete signal have been proposed. In addition, putting forward the concept of different set pairs provides effective mathematical tool, which more riches the construction of the perfect discrete signal. In this paper we will further research the construction methods of the different set pairs based on cyclotomy and Chinese Remainder Theorem and other perfect discrete signals such as quaternary sequences and quaternary sequence pairs.Firstly, based on cyclotomy and Chinese Remainder Theorem the difference set pairs search algorithms is proposed, and designed the difference set pairs search system based on cyclotomy and Chinese Remainder Theorem, which proposes the search function of the difference set pairs, and has been searched many difference set pairs. In addition, the system proposes validation functions of quaternary sequences with even period based on cyclotomic classes of order two and the quaternary sequence pairs with even period based on the reverse Gray mapping and interleaving technique.Secondly, by using the relevant nature of difference set pairs, cyclotomic classes and Chinese Remainder Theorem, we analyze many difference set pairs instances and get the associated regulars obtained in the instances. Many new methods for constructing difference set pairs have been put forward by studying and validating the regulars, the related proof and many examples of the new methods are given out. Those constructing methods not only enrich the theoretical research on difference set pairs, but also laid a solid foundation for later study.Thirdly, by studying the concept and the nature of the cyclotomic classes of order two and the application of the reverse Gray mapping, we can get a new construction method of quaternary sequences. While the distruction of quaternary sequences function values are decised by the parity of f in the cyclotomic classes of order two.Finally, by using the reverse Gray mapping and interleaving technique, a new methods for constructing quaternary sequence pairs with even period from two binary sequence pairs(u,v) and(x,y) with odd period has been proposed. While the distruction of quaternary sequence pairs function values are decised by the period and nature of the two binary sequence pairs.