The Constructions Of Difference Set Pairs Based On Cyclotomy

Twenty-first Century will be the era of spread spectrum communications,Whether in military communications,satellite communications,ranging and positioning,or in the field of digital mobile communications,it has produced a large amount of demand for ideal signal instances with good correlation properties.However,constraints on the construction of ideal sequences and sequence pairs,the known examples are far from being able to meet the increasing practical engineering requirements.Therefore,as an important combinatorial design tool,which is equivalent to the ideal two sequence pairs,the study of difference set pairs has become an important breakthrough.The purpose of this paper is to construct new instances of difference set pairs,the experimental results are obtained by the exhaustive search algorithm,and the theoretical proof is given based on the theory of cyclotomy.First of all,we introduce the basic knowledge and main properties of the classical cyclotomy theory,on the basis of this,the difference set pair search algorithm is implemented by computer programming.The algorithm runs in the way of exhaustive search,a large number of examples of unknown difference set pairs with high performance and high energy efficiency are obtained.Secondly,through the analysis of the experimental data,several new methods for constructing the difference set pairs based on the theory of circles are summarized,based on the comparative analysis of the composition of the cyclotomy,3 theorems of high energy efficiency difference set pairs are obtained.The energy efficiency of the two sequence pairs corresponding to these conclusions is also relatively high.Through the use of this kind of construction method,we can get a large number of instances of difference set pairs with high performance,and use these examples to construct the best complementary two sequence pairs,more data selection is provided for practical engineering requirements.Finally,based on the data of the experimental results,by using the method of odd order cyclotomy,we also get 4 new examples of difference set pairs which can be constructed by odd order cyclotomic method.There are corresponding rules of the form of the cyclotomy,4 theorems are summed up and the corresponding proof is given according to the theory of cyclotomic number.Through the combination of the theory and practice in this paper,can also continue to expand the scope of the search,then we get more and more examples of difference set pairs based on cyclotomy theory.In this paper,the difference set pairs can be obtained corresponding to the ideal two sequence pairs,through the in-depth study of the subject,it can also pave the way for the next research direction of constructing the ideal signal,in the conclusions of this paper,the work carried out in this paper and the next step is to focus on the description.