Theoretical Research On Almost Difference Set Pairs

Sequences and sequence pairs with good correlation,balance,high linearity complexity,etc excellent characteristics,can be used in radar,navigation,sonar,satellite communication,electronic countermeasures,information encryption,positioning,coded aperture imaging,and many other practical projects field.However,due to the difficulty of sequence and sequence pair existence conditions and direct construction methods,the study of sequences and sequence pairs has been limited.In recent years,scholars have found difference set pairs and almost difference set pairs that have an equivalent relationship with ideal binary sequence pair.Therefore,many scholars will study the hotspots of sequence pairs on the difference set pairs and almost difference set pairs.This paper constructs almost difference set pairs based on the two methods of the cyclotomic classes and the generalized cyclotomic classes.Firstly,two algorithms for the classical cyclotomic classes and the Z2v generalized cyclotomic classes are designed.The generalized cyclotomic classes is based on the combination of the classical cyclotomic classes and the Chinese remainder theorem.The cycle of generalized cyclotomic classes is longer than classical cyclotomic classes and has A wider search range.A large number of related data sets are obtained through computer search,which provides a data basis for the subsequent theorem summarySecondly,through the classical cyclotomic classes search almost difference set pairs even algorithm,the classical sub-circle class method is constructed to study the almost poor set pairs.Based on the 3-order,5-order,and 7-order cyclotomic classes,several construction methods for almost difference set pairs of v=3f+1,v=5f+1 and v=7f+1 three periods are proposed.Theoretical proof process are proposed.It provides new construction methods for the study of the almost difference set pairs of classical cyclotomic classes construction.Finally,the almost difference set pairs algorithm is searched by the generalized cyclotomic classes,and the almost difference set pairs are constructed by the generalized cyclotomic classes method.Based on the 3-order and 4-order generalized cyclotomic classes,several kinds of almost difference set pairs with periodic sums are proposed.The construction methods and the theoretical proof are provided to provide a new construction method for the study of the almost poor set couples of generalized cyclotomic classes construction.By the equivalence relation between the almost difference set pairs and the sequence pairs,the almost difference set pairs constructed in this paper can all correspond to the three-valued autocorrelation binary sequence pairs,which has practical significance for the study of ideal signals.