一类大集合容量伪随机序列集的线性复杂度研究

Study on Linear Span of a Pseudorandom Sequences Family with Large Family Size

具有大线性复杂度的序列可以抵抗Berlekamp-Massey算法攻击,提高数据的安全性,设计大线性复杂度伪随机序列是一个重要课题.使用d-齐次函数是增大序列的线性复杂度的一个有效方法.本文对正整数n=3m提出了一类周期为3n-1集合容量为3n的新序列集S(r),这里(r,3m-1)=1且1≤r<3m-1.通过取适当的参数r,精确地计算出了它的线性复杂度.

Application of sequences with large linear span can efficiently resist Berlekamp-Massey attack and im-prove security of data.The design of sequences with large linear span was an important research problem.A useful approach to construct sequences with large linear span was based on d-form function.For a positive integer n=3m, a sequences family S（r） with optimal correlation was proposed,where （r,3m-1）=1 and 1 ≤ r3m-1.By taking suit-able values of the parameter r, its linear span by in this paper was calculated accurately.