用广义布尔函数直接构造Z-互补偶
A Direct Construction of Z-Complementary Pairs Using Generalized Boolean Functions
摘要：
零相关区（ZCZ）比率，即，ZCZ的宽度和序列的长度的比率在降低通信系统的异步环境中的干扰方面起主要作用。然而，据作者所知，直接使用广义布尔函数（GBF）构造的偶数长度二进制Z-互补对（EB-ZCP）的最高ZCZ比是$\frac{2}{3}$。在这项研究中，我们提出了一个直接建设EB-ZCP通过GBF，它可以实现ZCZ比$\frac{3}{4}$。通常，所构造的EB-ZCP具有长度$2^{m-1}+2$，具有ZCZ宽度$2^{m-2}+2^{π(m-3)}+1$，其中pi是$m-2$变量上的置换。
英文摘要：
The zero correlation zone (ZCZ) ratio, i.e., the ratio of the width of the ZCZ and the length of the sequence plays a major role in reducing interference in an asynchronous environment of communication systems. However, to the best of the author's knowledge, the highest ZCZ ratio for even-length binary Z-complementary pairs (EB-ZCPs) which are directly constructed using generalized Boolean functions (GBFs), is $\frac{2}{3}$. In this research, we present a direct construction of EB-ZCPs through GBFs, which can achieve a ZCZ ratio of $\frac{3}{4}$. In general, the constructed EB-ZCPs are of length $2^{m-1}+2$, having a ZCZ width of $2^{m-2}+2^{π(m-3)}+1$ where pi is a permutation over $m-2$ variables.
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