Bent序列簇的迹表示

Trace representation of Bent sequence families

Bent序列簇主要通过线性满射和Bent函数来生成,但是长期以来,对其构造中使用的线性满射一直没有给出一个清晰的表达式。基于这一点,首先分析线性满射所满足的条件,再根据有限域的理论和m?序列的分布性质,给出它的具体表达式,从而得到Bent序列簇的迹表示;其次由Bent序列簇的迹表示和一类Bent函数构造了一类可快速生成的Bent序列簇。

Bent sequence families are mainly generated by a linear onto mapping and a bent function. Nevertheless, for a long time, the linear onto mapping has not an explicit expression. Firstly analyzing the conditions that the linear onto mapping must obey, then based on the theory of finite field and the distribution of m-sequences, the explicit expression of linear onto mapping is obtained. Therefore the trace representation of Bent sequences is gotten. Finally a family of Bent sequences is constructed which can be rapidly generated by the trace representation of Bent sequences and some Bent functions.