Autocorrelation of the Two-prime Sidelnikov Sequence
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摘要: Brandsttter等人(2011)结合割圆序列与Sidelnikov序列的概念定义了一个新序列双素数(p,q) Sidelnikov序列，并且分析了双素数Sidelnikov序列的均衡性、自相关函数、相关测度和线性复杂度轮廓，证明了双素数Sidelnikov序列有好的伪随机特性。该文主要研究d = gcd(p, q)=2的双素数Sidelnikov序列的自相关函数，借助于数论中的Legendre符号和有限域中的指数和理论，得到自相关函数的3个定理。通过与Brandsttter论文中自相关函数的界进行比较，本文定理2和定理3中的界O(q1/2)和O(p1/2)比Brandsttter的界O((p+q)/2)更紧，同时当p q或q p时，本文定理4中的界O((p q) 1/2)比Brandsttter的界O((p+q)/2+(p q) 1/2)更优。
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关键词:
- 双素数Sidelnikov序列 /
- 自相关函数 /
- Legendre符号 /
- 指数和
Abstract: Brandsttter et al. (2011) combined the concepts of the two-prime generator and Sidelnikov sequence to define a new sequence called two-prime (p, q) Sidelnikov sequence, and analyzed the balance, the autocorrelation, the correlation measure and the linear complexity profile of the sequence. They showed that this sequence has many nice pseudorandom properties. With the help of the Legendre symbol in number theory and the exponential sums in finite field, this paper investigates the autocorrelation of the two-prime Sidelnikov sequence with d=gcd(p, q)=2. Three theorems are got about the autocorrelation functions. The detailed comparison results show that the bounds O(q1/2) and O(p1/2) on the autocorrelation function in theorem 2 and theorem 3 are tighter than the Brandst?tters bound O((p+q)/2), besides, the bound O((p q) 1/2) in theorem 4 are tighter than the Brandsttters bound O((p+q) /2+(p q) 1/2) when p q or q p. -
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