Research On The Constructing Method Of Almost Difference Set Pairs Based On Difference Set Pairs

The ideal sequence has good correlation and high linear complexity,which has been a hot topic in the field of spread spectrum communication,coding theory and applied mathematics.However,it is far from satisfying the actual demand that the optimal sequence can be found in practical engineering.In order to solve this problem,a new form of optimal signal,sequence pairs,is proposed to greatly expand the existence space of the optimal discrete signal and provide more ideal signals for practical engineering.In this paper,we study the construction of almost difference sets by difference set pairs.Firstly,introducing the basic knowledge of difference set pairs and almost difference set pairs and giving the equivalence relation between difference set pairs and two-level binary sequence pairs.The theoretical basis is provided for the proof of the method that constructing almost difference set pairs based on difference set pairs.Then,this paper presents a new method that constructs almost difference set pairs based on difference sets pairs.The construction method is divided into two categories.One is minus element based on difference set pairs and the other is adding element based on difference set pairs.It is proved in theory,and through the computer finds some specific examples.Through these examples can get some three-level binary sequence pairs with good correlation,extending the existing space of ideal sequence.Finally,analyzing the construction method of minus two elements based on difference set pairs,the construction method of adding two elements based on difference set pairs.The algorithm is designed to search the almost difference sets obtained by this construction method.At the same time,the results will be found in table.The experimental results obtained by the system provide support for further research.