Balanced optimal almost binary sequence pairs of period N≡1（mod4）

Xiuping PENG; Hongxiao LI; Shide WANG; Hongbin LIN

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

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Balanced optimal almost binary sequence pairs of period N≡1（mod4）

Papers | 更新时间：2024-06-05

- Balanced optimal almost binary sequence pairs of period N≡1（mod4）
- Journal on Communications Vol. 42, Issue 12, Pages: 163-171(2021)
- 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：
- 基金信息：
  
  The National Natural Science Foundation of China(61601401);The Natural Foundation of Hebei Province(F2021203040);Young Talent Program of Colleges in Hebei Province under Grant(BJ2018018);Young Talent Program of Colleges in Hebei Province under Grant(ZD2019039);The Research and Technology in Higher Education of Hebei(QN2021144)
- DOI：10.11959/j.issn.1000-436x.2021078
  CLC： TN911.2
- Online First：2021-12，
  
  Published：25 December 2021
- 稿件说明：
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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：

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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