Research On Construction Methods Of Almost Difference Set Pairs Based On Generalized Cyclotomic Class And Difference Set Pairs

In signal design,signals with good autocorrelation can distinguish their own signals from their delay signals.Deeply exploring the optimal discrete signal can not only provide support in theoretical design,but also provide guidance for practical applications.With the continuous research of scholars on sequence,sequence pairs,difference set,and difference set pairs,almost difference set pairs have gradually entered people’s vision and become one of the directions for studying discrete signals.The thesis mainly focuses on the study of almost difference set pairs and proposes two new methods for constructing almost difference set pairs.Firstly,two search algorithms for almost difference set pairs are designed.The first algorithm is to use the generalized cyclotomic class of order 2-3 and the Chinese remainder theorem to search for almost difference set pairs;The second algorithm uses the definitions of difference set pairs and almost difference set pairs to search for the data of difference set pairs and almost difference set pairs,and combines the obtained data in pairs to construct new almost difference set pairs.Secondly,a method is proposed to construct almost difference set pairs based on the generalized cyclotomic class of order 2-3 and the Chinese remainder theorem.Based on the obtained data of almost difference set pairs,conduct a detailed analysis and organization,and promote it.In two different cases,p ≡1(mod4)and p ≡3(mod4),obtain the theorems for almost difference set pairs with period 7 p,and prove it.In addition,by using the equivalence relation between almost difference set pairs and three-level autocorrelation binary sequence pairs,it is concluded that the characteristic sequence pairs corresponding to these almost difference set pairs have optimal three-level autocorrelation function values.Finally,a method for indirectly constructing almost difference set pairs is proposed.Based on the definitions and properties of difference set pairs and almost difference set pairs,it is concluded that under certain conditions,difference set pairs and difference set pairs,difference set pairs and almost difference set pairs,almost difference set pairs and almost difference set pairs can all be constructed into new almost difference set pairs.At the same time,examples of almost difference set pairs corresponding to these three indirect construction methods are given.In this thesis,two new methods for constructing almost difference set pairs are proposed,which extend the existence range of almost difference set pairs,providing new ideas for further in-depth research on the construction methods of almost difference set pairs,and also laying the foundation for future research on discrete signals.