Research On The Construction Method Of Almost Difference Set Pairs

Sequence pairs with ideal autocorrelation properties,balance and high linear complexity have many applications in many fields such as radar,sonar,navigation,synchronization,electronic countermeasure,telemetry,remote control,information enctyption,acoustic imaging and so on.However,it is difficult to construct the ideal sequence pairs directly,scholars often use the mathematical tools such as the difference set pairs and almost difference set pairs.Aiming at the shortcoming of existence almost difference set pairs on small space can not meet the actual needs of the project methods for the construction of almost difference set pairs based on the Cyclotomic,Whiteman generalized cyclotomic and Chinese remainder theorem.Firstly,present two construction methods for constructing almost difference set pairs based on the Cyclotomic and the Whiteman generalized cyclotomic,the algorithm is designed and the algorithm flow chart is drawn based on the definition of the theory of almost difference set pairs and the theory of Chinese remainder theorem;design the database,data table about algorithm,write pogram.Through computer search,a large number of almost difference set pairs are obtained,which provides the data base for the subsequent research of almost difference set pairsSecondly,according to almost difference set pairs,properties of Cyclotomic,the cyclotomic numbers,the lemma about Cyclotomic and the obtained experimental data of almost difference set pairs,summarize the methods of almost difference set pairs with period v=3f+1 and v=5f+1 based on Cyclotomic,several almost difference sets with the same parameter form are obtained,and the proofs are given by using relevant knowledge.Finally,based on the analysis of the experimental data of the algorithm for constructing almost difference set pairs by using the Whiteman generalized cyclotomic.The method of constructing almost difference set pairs based on Whiteman generalized circle is obtained,and almost difference set pairs is proved by using the number and properties of Whiteman generalized cyclotomic.In this paper,the almost difference set pairs can be obtained some binary sequence pairs with three-level autocorrela-tion,the construction method of almost difference set pairs is the theoretical basis for studying ideal signals.In the conclusions of this paper,the work carried out in this paper and the next step is to focus on the description.