周期为N≡1（mod4）的平衡最优几乎二元序列对

彭秀平; 李红晓; 王仕德; 林洪彬

doi:10.11959/j.issn.1000-436x.2021078

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周期为N≡1（mod4）的平衡最优几乎二元序列对

学术论文 | 更新时间：2024-06-05

- 周期为N≡1（mod4）的平衡最优几乎二元序列对
- Balanced optimal almost binary sequence pairs of period N≡1（mod4）
- 通信学报 2021年42卷第12期页码：163-171
- 作者机构：
  
  1. 燕山大学信息科学与工程学院，河北秦皇岛 066004
  2. 河北省信息传输与信号处理重点实验室，河北秦皇岛 066004
  3. 燕山大学电气工程学院，河北秦皇岛 066004
- 作者简介：
  
  [ "彭秀平（1984- ），女，安徽安庆人，博士，燕山大学副教授，主要研究方向为编码理论、信号设计等" ]
  [ "李红晓（1995- ），女，河北邢台人，燕山大学硕士生，主要研究方向为编码理论、信号设计等" ]
  [ "王仕德（1997- ），男，河北石家庄人，燕山大学硕士生，主要研究方向为编码理论、信号设计等" ]
  [ "林洪彬（1979- ），男，河北秦皇岛人，燕山大学副教授，主要研究方向为智能信息处理、动态复杂场景认知" ]
- 基金信息：
  
  国家自然科学基金资助项目(61601401);河北省自然科学基金资助项目(F2021203040);河北省高等学校青年拔尖人才计划基金资助项目(BJ2018018);河北省高等学校科学技术研究基金资助项目(ZD2019039);河北省高等学校科学技术研究基金资助项目(QN2021144)
- DOI：10.11959/j.issn.1000-436x.2021078
  中图分类号： TN911.2
- 网络出版日期：2021-12，
  
  纸质出版日期：2021-12-25
- 稿件说明：
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彭秀平, 李红晓, 王仕德, 等. 周期为N≡1（mod4）的平衡最优几乎二元序列对[J]. 通信学报, 2021,42(12):163-171.

Xiuping PENG, Hongxiao LI, Shide WANG, et al. Balanced optimal almost binary sequence pairs of period N≡1（mod4）[J]. Journal on communications, 2021, 42(12): 163-171.
彭秀平, 李红晓, 王仕德, 等. 周期为N≡1（mod4）的平衡最优几乎二元序列对[J]. 通信学报, 2021,42(12):163-171. DOI： 10.11959/j.issn.1000-436x.2021078.

Xiuping PENG, Hongxiao LI, Shide WANG, et al. Balanced optimal almost binary sequence pairs of period N≡1（mod4）[J]. Journal on communications, 2021, 42(12): 163-171. DOI： 10.11959/j.issn.1000-436x.2021078.

摘要

基于组合设计理论，对周期为N≡1（mod 4）的平衡最优几乎二元序列对的构造方法进行了研究。根据（几乎）二元序列对的不同组合，得出了最大互相关值分别为θ

=1，2，3，以此θ

值为前提，推导得出 3 种情况的自相关理论界，并生成了4类满足互相关值和自相关理论界下界值的平衡（几乎）最优几乎二元序列对。所提构造方法扩展了互相关值的取值范围并进一步降低了最优二元序列对的互相关值，且序列长度参数 f 可选择任意整数，丰富了最优二元序列对的存在空间。

Abstract

Based on the combinatorial design theory， the constructions of balanced optimal almost binary sequence pairs of period N≡1（mod 4）were researched.The maximal cross-correlation values θ

were obtained by different combinations of （almost） binary sequence pairs.Furthermore， three new bounds on the autocorrelation values under the precondition of the value of θ

=1，2，3 were presented individually.Meanwhile，four types of balanced（almost）optimal almost binary sequence pairs were generated， which satisfied the cross-correlation values and autocorrelation theory bounds.Through the constructions， the range of the cross-correlation values is expanded and the cross-correlation value of the optimal binary sequence pairs is further reduced.More than odd， the value of sequence length parameter f can be any integer， which enriches the existence space of the optimal binary sequence pair.

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references

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