Abstract: For a prime p=3 and even n=2k，a family of nonbinary sequences S^(r) with period 3ⁿ-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.

Key words: sequences, correlation function, linear span

摘要： 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3^k-1互素。这类序列集的相关函数取-1±3^k，-1，-1+2•3^k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。

关键词: 序列, 相关函数, 线性复杂度