On Bent Sequences And The Distribution Of Its Correlation Value

Periodic sequences with good pseudo-random characteristic and low cross-correlation have important applications in code division multiple access(CDMA)communication and cryptography. Bent function sequence set is a kind of excellent sequence set. It not only has good cross-correlation property, but also has high linear complexity, which plays an important role in code division multiple access(CDMA)communication and cryptography system.In this paper,we mainly study the following problems and innovation points:(1)we study the construction methods of Generalized Binary Bent sequences systematically, prove that all kinds of the bent sequence sets have the same correlation distribution, and clearly show the correlation distribution of any Generalized Binary Bent sequence;(2) we verify several bent function in detail, and construct several new bent function sequence sets through the use of the bent function in the middle field;(3) Based on the idea that enlarge the family size of Bent sequence sets, we study the construction methods of multiple bent sequence sets and clearly prove the correlation distribution of multiple bent sequence sets by using algebraic method. In the same time,we put forward the concept of Bent function with intensity of |B|. By choosing appropriate bent functions, we construct multiple bent sequence sets with good correlation and large number. The results show that under certain conditions, the cross-correlation value of two different bent sequences which from different bent sequence sets is large in one shift and is less than the maximum cross-correlation value of the original bent sequence set in the other shift,therefore constructing a larger number of bent sequence sets which have more important application value and correcting some existing results.