Research On Constructing Method And Searching Algorithm Of Difference Set Pairs

The perfect discrete signal and its design plays an increasingly important role in most field theoretically and practically, such as in modern communications, radar, sonar, navigation, space ranging and controlling, electronically countermeasures, and the design optimization of other wired and wireless systems. Well-structured signals can not only increase data confidentiality, but also enhance system's properties of anti-interference, anti-jamming capability. Over the past decades, the research has made great achievements, but there were some deficiency, so the further in-depth study is underway at present.Firstly, in the research into Cyclotomic class, difference set pairs based on six order Cyclotomic class is presented. And the constructing method has general applicability. Moreover, through the analysis on relations between difference set pairs and binary array pairs, more perfect binary array pairs will be structured based on difference set pairs. All these results provide wider range for engineering application, in the mean time, the constructing method of difference set pairs lays theoretical foundation for further study on difference set pairs.Secondly, based on the analysis on Multiplier Theorem, an in-depth research into difference set pairs was done and as a result, orbit search algorithm were given. Two orbit principles are deduced and given as theorems, when the order of Abel group can be described by the product of 3 and a prime. Moreover, the non-existence of a kind of difference set pairs is proved .This theorem can easily judge the non-existence of difference set pairs with given parameter.Finally, optimization search algorithm is presented in the study, which integrates orbit disciplines and Multiplier Theorem and Multiplier guess based on difference set pairs and greatly increases the search efficiencies of algorithm. Through this algorithm, the previous unknown difference sets pairs are searched in the study. It not only provides more instances of difference set pairs for engineering application, but also lays theoretical foundation for Multiplier Guess based on difference set pairs.