一类具有低相关特性和较大线性复杂度的序列集

Family of sequences with low cross-correlation and large linear span

对于p=3和偶数n=2k,构造了一类周期为3n-1大容量序列集S(r),这里r与3k-1互素。这类序列集的相关函数取-1±3k,-1,-1+2·3k四值,并完全确定了相关值的分布。通过选取适当的参数r,证明了这类序列集具有较大的线性复杂度下界。

For a prime p=3 and even n=2k,a family of nonbinary sequences S^（r） with period 3^n-1 and large family size is proposed in this paper,where r relatively primes to 3^k-1.The presented family has 4-valued out-of-phase auto- and cross-correlation values -1±3^k,-1,-1＋2·3^k,and correlation distribution of the family is determined.These sequences in this family can achieve large lower bound of linear span by choosing a suitable parameter r.