李恒智 赵伟 王东 贾彦国 沈秀敏

摘 要：

具有理想自相關性、平衡性和易于实现特性的四进制序列，广泛应用于通信等领域中。虽然已被发现的平衡理想自相关四进制序列有很多，但低相关四进制序列还有很大的研究空间。本文基于广义四阶分圆类和中国剩余定理对周期为2p（p=4f+1奇素数）的低相关四进制序列进行研究，当四进制序列的第0位和第p位元素值分别同时为1和i时，得到了旁瓣值为{2，-2，-6}、{2，-2，-4，4}的平衡低相关四进制序列，当第0位和第p位元素值分别同时为-1和-i时，得到了旁瓣值同为{2，2i，-2i，-2+2i，-2-2i}的平衡低相关四进制序列。

关键词：

低相关四进制序列；广义分圆类；中国剩余定理；平衡

中图分类号：TN911.2  文献标识码： A  DOI：10.3969/j.issn.1007-791X.2023.01.010

3 结论

本文通过利用广义四阶分圆类和中国剩余定理得到了偶周期为2p（p=4f+1奇素数）的平衡低相关四进制序列。通过本文的研究总结，进一步扩大了四进制序列的范围，对于推进研究基于四进制序列的最佳离散信号有重要意义。

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Construction on low-correlation quaternary sequences with period 2p

LI Hengzhi1，ZHAO Wei2，3，WANG Dong2，JIA Yanguo2，SHEN Xiumin2

（1.Hebei Institute of International Business and Economics，Qinhuangdao，Hebei 066311，China;

2.School of Information Science and Engineering，Yanshan University，Qinhuangdao，Hebei 066004，China;

3.Liren College，Yanshan University，Qinhuangdao，Hebei 066004，China）

Abstract：

The quaternary sequence with the characteristics of ideal autocorrelation，balance and easy realization is widely used in the field of communication.Although many balanced ideal autocorrelation quaternary sequences have been found，there is still much room for research on low-correlation quaternary sequences.Based on the generalized cyclotomic class and the Chinese remainder theorem，a quaternary sequence with a period of 2p （p=4f+1 is odd prime number） is studied.When the 0th and pth element values of the sequence are 1 and i，a balanced low-correlation quaternary sequence with side-lobe values of {2，-2，-6}、{2，-2，-4，4}are obtained.When the 0th and pth element values of the sequence are -1 and -i，a balanced low-correlation quaternary sequence with side-lobe values of{2，2i，-2i，-2+2i，-2-2i} are obtained.

Keywords：

low-correlation quaternary sequence;generalized cyclotomic classes;Chinese remainder theorem;balance