Research On Difference Set Pairs Construction Method And The Track Rules

Correlation function also has good properties and high linear complexity of the ideal sequence in radar, sonar, synchronization, channel estimation and balance, confidentiality of communications, test and measurement, coded aperture imaging, and many other engineering fields has important applications, including sequence pairs design a more ideal structure is an important breakthrough in the direction of the sequence, but even worse is the set of new sequences for the sequence pairs design of such mathematical tools. But also made a variety of difference set pairs and the construction method, but even the known number of difference set is not enough, yet can not meet the engineering needs.This paper analyzes the nature of the cyclotomic class concept and meaning of difference set pairs, according to the order of the lower class of cyclotomic difference sets constructed features dual approach, from the convenience, accuracy and versatility of the direction of paper proposes three Cyclotomic difference sets dual class constructor, and not limit the number of cyclotomic order may be constructed directly cyclotomy a lot of difference set pairs.While this difference set for the dual use of the track to determine some of the difference set pairs and there is no problem and track law-depth study. First, computer searches a large number of poor track data set pairs, based on the summary of its analysis, based on multipliers, the order of groups such as the classification of the different conditions, the order of the group is small, the proposed The corresponding number of each track length and the law; Second, for relatively large order of cases, respectively, summed up the forms and parameters of the corresponding difference set pairs the track rules; Finally, we get the orbit of the law of a general theorem, as long as The order of a given group and the associated prime in the multiplier, you can quickly get the length and number of each track.For the application of the results of these studies, the paper behind each theorem are given by the corresponding application example, the final summary and analysis of problems for further research provides direction and valuable experience.