The Constructions Of Almost Difference Set Pairs Based On Cyclotomy And Generalied Cyclotomy

Ideal sequence has been applied in modern communication, spread spectrum address code, cryptography, and engineering areas such as mathematics, because it has the good characteristics of correlation function, in addition, the height of the linear complexity is also a criteria for measuring sequence, these have always been the hot spot of the scholars in the study of signal problem. The number of ideal sequence is very limited, however, in its application domain can’t meet the actual needs. So predecessors proposed the concept of the sequence pairs, the structure of the various forms of sequence pairs has become an important direction of research optimal discrete signal. Due to the almost difference set pairs is equivalent to the almost perfect autocorrelation binary sequence pairs, so the purpose of this article is to construct new almost difference set pairs, its structure is the use of cyclotomic class and generalized cyclotomic class.First of all, almost difference set pairs search algorithm based on the given cyclotomic class and twice prime v residue class ring vZ2 of generalized cyclotomic class is given, the algorithm realized the function of search almost difference set pairs, by the style of the computer search, respectively obtained by cyclotomic class structure of almost difference set pairs experimental data and by generalized cyclotomic class structure of almost difference set pairs experimental data.Secondly, on the analysis of the experimental data of a lot of almost difference set pairs, after summarizing the various almost difference set pairs cyclotomic class constructor, these construction method including the order 2, 4 and 6 cyclotomic the get method, expand the space of almost difference set pairs.Finally, based on the analysis of the definition and properties of the generalized cyclotomic class, after a high degree of integration to the experimental results of the almost difference set pairs, it is concluded that a variety of construction methods of almost difference set pair. By almost difference set pairs’ s construction based on generalized cyclotomic class is made from the prime number area expanded to 2 times, by the almost difference sets pairs concluded that the existence space of sequence is expanded, thus enriched the existence of the discrete signal.