Research On Binary Complementary Sequence And Binary Complementary Sequence Pairs

This research belong to the realm of Perfect signals, Perfect signals are widely used in mordern engineering such as communication system and navigation system. In practice the demands of practical engineering are so various that there haven't any criterion of the perfect signals that can adapt to all kinds of engineering, so there have not a clear defmation of perfect signals. All the signals that can be used in practical engineering bestly are called perfect signals. Now the most primary rules of the perfect signals include periodic correlation, aperiodic correlation and hanming correlation and so on.Complementary sequences are the most representative perfect signals that have good aperiodic correlation feature. The binary complementary sequences were introduced in 1949. Now the research of it has made a great achievement, based on it we studied the feature of the binary complementary sequences. The feature sequences of complementary sequences are introduced in this paper. Every complementary sequence has two kinds of feature sequences. Each equivalence class has 64 or 32 complementary sequences. When the length of complementary is not less then 4, it can determine which equivalence class has 64 or 32 by the feature sequences of this class. When the complementary sequences can be constructed, it is called constructible complementary sequence. Now there are 5 constructive methods have been found, through which all of the complementary sequences whose length is 2'10s26' can be constructed. It was proved in this paper that it can determine which equivalence class is constructible or not by the feature sequence. Based on the reseach and computer we have got all the equivalence complementary sequence class with length of not more than 40, and found a new complementary sequences kernel with length of 20.Complementary sequence pair is an evolvement shap of complementary sequences. As a new type of perfect signal, the complementary sequence pairs would possibly have good future application in communication engineering. The property of complementary sequence pairs is studied, and a new denotation figured by three sequences is introduced in this paper. We also deduced the maximum of correlative function of the odd length complementary sequence pairs. On the basis of the property that was found in this paper we have designed a searching arithmetic. Then we have searched out all of the unequal complementary sequence pairs with length up to 20. We have got some suppositions from the searching results, though the correctness of it is waiting for prove.