周期为4v(几乎)平衡理想二进制序列构造研究  

Study on the Constructions of Balanced Optimal Binary Sequences with Period 4v(almost)

作　　者：彭秀平[1,3,4] 冀惠璞 林洪彬 刘刚[1] PENG Xiuping;JI Huipu;LIN Hongbin;LIU Gang(School of Information Science&Engineering,Yanshan University,Qinhuangdao 066004,China;School of Electrical Engineering,Yanshan University,Qinhuangdao 066004,China;Hebei Province Key Laboratory of Information Transmission and Signal Processing,Qinhuangdao 066004,China;Key Laboratory of Communication Network Information Transmission and Distribution Technology,Shijiazhuang 050081,China)

机构地区：[1]燕山大学信息科学与工程学院,秦皇岛066004 [2]燕山大学电气工程学院,秦皇岛066004 [3]河北省信息传输与信号处理重点实验室,秦皇岛066004 [4]通信网信息传输与分发技术重点实验室,石家庄050081

出　　处：《电子与信息学报》2022年第1期271-278,共8页Journal of Electronics & Information Technology

基　　金：国家重点研发计划(2017YFB0306402);河北省自然科学基金(F2021203040,E2020203188);河北省高等学校科学技术研究基金(BJ2018018,ZD2019039,QN2019133);弹性网络服务自主适应管控技术研究(6142104190109)。

摘　　要：具有理想自相关特性的序列在无线通信、雷达以及密码学中具有重要的作用。因此为了扩展更多可应用于通信系统的理想序列,该文基于2阶分圆类和中国剩余定理,提出3类新的周期为T=4v(v是奇素数)平衡或几乎平衡理想二进制序列构造方法。构造所得序列的周期自相关函数满足:当v≡3(mod 4)时,序列的周期自相关函数旁瓣值取值集合为{0,-4}或{0,4,-4};当v≡1(mod 4)时,相应的取值集合为{0,4,-4}。通过该文方法拓展了周期为4v平衡理想二进制序列的存在范围,从而可为工程应用提供更多性能优良的理想序列。Sequences with optimal autocorrelation property have important roles in wireless communication,radar and cryptography.Therefore,in order to expand more ideal sequences that can be applied to communication systems,based on cyclotomy of order 2 and Chinese remainder theorem,three new constructions of balanced or almost balanced binary sequences of period T=4v(v is odd prime)are presented in this paper.The periodic autocorrelation function of the constructed sequence satisfies:when v≡3(mod 4),the out-of-phase autocorrelation value set of the sequence is{0,-4}or{0,4,-4};whenv≡1(mod 4),the corresponding value set is{0,4,-4}.The existing range of balanced optimal binary sequences with period of 4v is extended by this method,so that more optimal sequences with good property can be provided for engineering applications.

关 键 词：二进制序列 几乎差集 分圆 理想自相关性 

分 类 号：TN911.2[电子电信—通信与信息系统]