一类广义分圆三元序列的自相关值和线性复杂度

The Autocorrelation Values and Linear Complexity of a Class of Generalized Cyclotomic Ternary Sequence

摘要: 具有良好性质的伪随机序列在信息安全与通信中有广泛的应用。根据广义分圆定义构造了一类周期为pⁿ⁺¹的几乎平衡的6阶广义分圆三元序列。利用经典的6阶分圆数和部分指数和进一步计算了该序列的自相关值和线性复杂度。结果表明该序列有较好的线性复杂度。

Abstract: Pseudorandom sequences with good properties have wide application in information security and communications et al. This paper construct an almost balanced generalized cyclotomic ternary sequence with period pⁿ⁺¹ based on the definition of generalized cyclotomic. Further, the autocorrelation values and linear complexity of this sequence are calculated. The method are based on using the classical cyclotomic numbers of order six and the values of partial exponential sums of cyclotomic class of order six over an extension field of GF(3). Results show that this sequence possesses good linear complexity.