关于第二类Bent基和线性基Bent序列的讨论

On the Second-Class Concatenating Bent Functions

C.M.A dam s和S.E.T avares在1990年曾猜测所有长为2n的Ben t序列都是由2n-2个长为4的Ben t序列或2n-2个长为4的仿射序列级联而成,并分别称这样的Ben t序列为Ben t基的和线性基的,1991年郭宝安和蔡长年通过构造一类非Ben t基非线性基的Ben t序列否定了该猜想.文章考虑用4个长为2n-2的(1,-1)-序列级联构造Ben t序列的问题,并称之为第二类级联,给出第二类线性基Ben t序列的类型以及级联序列为第二类Ben t基Ben t序列的一个充分条件.

Concatenation has been being a very important method to construct Bent sequences （or functions）. Adams ＆ Tavares, Guo ＆ Cai discussed the first-class Bent-based and linearbased Bent functions in early 1990＇s respectively. In this paper the Bent sequence concatenated by four Bent sequences or linear sequences of length 2^（n-2） was considered. A criterion for the second-class Bent-based Bent sequence was obtained, and the all forms of the second-class linear-based Bent sequences were found.