Research On Construction Method Of Difference Set Pair And Almost Difference Set Pair Based On Generalized Cyclotomic

In recent decades,distributed spectrum communication system has been widely used in Bluetooth,ranging and positioning,mobile broadband,civil digital beehive and other fields because of its advantages of good anti stealth,strong anti-interference ability and low electromagnetic interference.The performance of synchronization,anti-jamming,anti interception and multiple access communication of distributed communication system is closely related to the characteristics of spread spectrum sequence used in the system.This is the reason why we study and promote the concept of sequence design.Therefore,the design of high performance spread spectrum sequence is of great theoretical significance and practical value to improve the performance of modern distributed spectrum communication system.In recent years,researchers have found difference set pairs and almost difference set pairs which are equivalent to binary autocorrelation binary sequence pairs and ternary autocorrelation binary sequence pairs.Due to the small number of sequence pair spread spectrum codes,the construction methods of difference set pairs and almost difference set pairs in spread spectrum sequence pairs are studied based on the theory of generalized cyclotomic class,Chinese Remainder Theorem and Cartesian product.Firstly,the generalized cyclotomic method is introduced and a difference set pair search algorithm based on Generalized Cyclotomic with period is designed.The sum is a different odd prime number.The difference set pairs with the parameter form of,etc.are constructed by using the generalized cyclotoms of order 2-2.Then the binary autocorrelation binary sequence pairs are obtained according to the equivalence relationship between the binary autocorrelation binary sequence pairs and the difference set pairs.Secondly,an almost difference set pair search algorithm based on 2-2 order generalized cyclotoms with period is designed.The almost difference set pairs with parameters of,etc.are obtained,and then the almost optimal autocorrelation binary sequence pairs,namely ternary autocorrelation binary sequence pairs,are obtained.Inspired by the difference set pair search algorithm mentioned above,this algorithm applies the generalized cyclotomic method based on to search more types of sequence pairs,and constructs more types of Cyclotomic classes according to different cyclotomic orders.In addition,the search range of sequence length is extended.Finally,the experimental results of the above two algorithms are summarized,and a variety of general rules of constructing difference set pairs and almost difference set pairs are found.Combined with Chinese Remainder Theorem and the calculation formula of Cyclotomic number,the detailed proof process is given.The construction method used in this paper is not only suitable for difference set pairs and almost difference set pairs,but also points out a new direction for the development of other types of sequence pairs,which has important practical significance for the study of discrete signals.