由已知Bent序列构造新的Bent序列

从Bent函数的序列表示出发,通过对Walsh-Hadamard矩阵性质的研究,得到了n阶Walsh-Hadamard矩阵Hn的每一行取反向及隔位取负仍为该矩阵的某行,任一行的奇数位项及偶数位项为n-1阶Walsh-Hadamard矩阵Hn-1的某行,由此给出了由两个已知Bent序列,通过不同的级联构造Bent序列的三种方法,并得到了由4个Bent序列级联而成的序列为Bent序列的充要条件为:该级联序列中的前两个序列及后两个序列的插位构成的序列为Bent序列.

Constructing Bent Sequence from Given Bent Sequences

Based on the sequences representation of Bent functions,this paper proves that when each line of the n-order Walsh-Hadamard matrix Hn is taken reverse and negative,it is still being a line of the former matrix.It also proves that any line of the even and odd items is a line of the n-1-order Walsh-Hadamard Matrix Hn-1.Secondly,this paper proposes three methods of constructing Bent sequences through two different concatenation by two existing bent sequences.Lastly,this paper proves that the sequences which are concatenated by four Bent sequences are Bent sequences if and only if the sequences composed by the first two sequences and the later two ones insertion in the concatenatine sequences are Bent sequences.