| The ideal sequence with good autocorrelation properties and high linear complexity features is applied in many areas of engineering and science such as communication, radar and so on. However, according to the results of the current study, the existence conditions, application mode and further of the perfect sequences make it can not meet the actual needs of the project. It leads to propose a new sense of perfect signal form urgently. Thus, the concept of " pairs " have come into being. The design and constructions of sequence pairs becomes an important breakthrough in the direction of constructing more and more ideal sequence. In this paper, we mainly study on the almost difference set pairs that is a mathematical tool for sequence pairs and ternary sequence pairs and quaternary sequence pairs also with good autocorrelation properties, then put forward the construction methods.Firstly, by studying the concept and the nature of cyclotomic classes, get the program of the base cyclotomic numbers, and propose the cyclotomic formulas of arder 2ã€4ã€6. At the same time, they provide a strong mathematical support for the constructing of almost difference set pairs and ternary sequence pairs based on cyclotomic.Secondly, propose the almost difference set pairs search algorithms and the ternary sequence pairs search algorithms based on cyclotomy, get amount of experimental data, which lay a foundation for proposing new constructions of almost difference set pairs and ternary sequence pairs.Finally, through extensive reading related literatures, on the base of the binary sequence pair, theory to deduce "cyclic shift method" "zero method" two new methods to construct the ternary sequence pairs and quaternary sequence pairs.The presence of these construction method is not only enriched the sequence pairs also got more forms of mathematical support tools for the sequence pairs, at the same time, they provide the ideal signal for the actual engineering needs. |
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