A Family of Polyphase Sequences With Asymptotically Optimal Correlation
A Family of Polyphase Sequences With Asymptotically Optimal Correlation
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DOI：
10.1109/tit.2018.2796597
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发表时间：
2018-01
影响因子：
2.5
通讯作者：
Zhengchun Zhou;T. Helleseth;U. Parampalli
中科院分区：
文献类型：
--
作者：
Zhengchun Zhou;T. Helleseth;U. Parampalli
相关性低的序列在通信，雷达和密码学中具有重要的应用。在本文中，提出了使用有限字段$ {\ mathrm {f}} _ {q} $上的加法和乘法字符的简单结构。该构建适用于任何有限字段$ {\ mathrm {f}} _ {q} $，$ q> 2 $，并生成一个$ q-1 $序列的家庭，带有$ q-1 $，最大相关性$ \ sqrtt {q} $。对于众所周知的韦尔奇结合，这个家庭在渐近上是最佳的。最值得注意的是，该家族中每个序列的最大自相关幅度等于1，并且每个不同的序列彼此正交。还建立了该家族的相关幅度的分布。
Sequences with low correlation have important applications in communications, radar, and cryptography. In this paper, a simple construction of polyphase sequences using additive and multiplicative characters over the finite field ${\mathrm {F}}_{q}$ is proposed. The construction works for any finite field ${\mathrm {F}}_{q}$ with $q>2$ and generates a family of $q-1$ sequences with period $q-1$ and maximum correlation $\sqrt {q}$ . This family is asymptotically optimal with respect to the well-known Welch bound. Most notably, the maximum autocorrelation magnitude of each sequence in this family is equal to 1, and every two distinct sequences are orthogonal to each other. The distribution of the correlation magnitudes of this family is also established.