Research On The Construction Of Almost Difference Set Pairs

In the spread spectrum communication system,the quality of the spread spectrum sequence affects the quality of communication,in order to find a good sequence,the concept of the best sequence,sequence pair and so on has been proposed.To expand the existence space of ideal sequence pairs,the definition of three-level autocorrelation binary sequence pairs is proposed.Because almost difference set pairs are equivalent to three-level autocorrelation binary sequence pairs,almost difference set pairs become an important tool to study three-level autocorrelation binary sequence pairs.In this paper,two computer search algorithms are used to construct almost difference set pairs.Firstly,this paper proposes an algorithm to construct almost difference set pairs by subtracting or adding elements to the difference sets,and uses the 8th and 10 th order classical cyclotomic algorithms,and adds multithreading method in the programming,and searches out many almost difference set pairs data by computer.Secondly,after summarizing the data obtained by the increasing and decreasing elements of difference sets search algorithm,three theorems are summed up for the methods of reducing and increasing elements respectively,and the theorem is proved by the definitions of difference sets and almost difference set pairs.The examples of corresponding theorems and the correlation function values of almost difference set pairs are given.Some corollaries are also drawn in the process of proof.Finally,this paper summarizes the data obtained by the classical circle division search algorithm,summarizes four theorems for the methods of 8-order and 10-order circle division respectively,and proves the theorem by the definitions and properties of circle division,circle division number and so on.In each theorem,examples are also given.Because the proof is similar,some theorems omit the proof and give the conclusion directly in the table.