周期为2q理想几乎四进制序列构造研究

doi:10.11959/j.issn.1000-436x.2019225

通信学报 ›› 2019, Vol. 40 ›› Issue (12): 105-113.doi: 10.11959/j.issn.1000-436x.2019225

周期为2q理想几乎四进制序列构造研究

彭秀平^1,²,冀惠璞^1,²,郑德亮^1,²,牛晓霞^1,²

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

修回日期:2019-09-26 出版日期:2019-12-25 发布日期:2020-01-16
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|冀惠璞（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|郑德亮（1994- ），男，四川巴中人，燕山大学硕士生，主要研究方向为编码理论、信号设计等|牛晓霞（1981- ），女，河北保定人，燕山大学高级实验师，主要研究方向为图像信息处理、三维建模等。
基金资助:
国家自然科学基金资助项目(61601401);国家自然科学基金资助项目(61601399);河北省高等学校青年拔尖人才计划基金资助项目(BJ2018018)

Study on the constructions of optimal almost quaternary sequences with period 2q

Xiuping PENG^1,²,Huipu JI^1,²,Deliang ZHENG^1,²,Xiaoxia NIU^1,²

¹ School of Information Science ＆Engineering,Yanshan University,Qinhuangdao 066004,China
² Hebei Province Key Laboratory of Information Transmission and Signal Processing,Qinhuangdao 066004,China

Revised:2019-09-26 Online:2019-12-25 Published:2020-01-16
Supported by:
The National Natural Science Foundation of China(61601401);The National Natural Science Foundation of China(61601399);Young Talent Program of Colleges in Hebei Province under Grant(BJ2018018)

摘要/Abstract

摘要：

基于中国剩余定理和四阶分圆类，对周期为N=2q(q为奇素数)的几乎四进制序列的构造方法进行了研究。根据序列y的y(0)和y(q)2个位置含0的个数对序列进行分类，构造得到了旁瓣值分别为{0,-2}、{0,2,-2}、{0,-2,-2i,2i}，且具有好的平衡性的3类理想几乎四进制序列。所提构造方法得到的序列具有良好的自相关性和平衡性，扩大了现有理想平衡四进制序列的存在范围，为实际应用提供了更多性能优良的序列。

关键词: 四进制序列, 理想几乎四进制序列, 平衡序列, 分圆类

Abstract:

Based on the Chinese remainder theorem and cyclotomic classes of order 4,the constructions of almost quaternary sequences with period N=2q (where q is an odd prime) was studied.According to the number of “0” in the two positions y(0) and y(q),three types of optimal almost quaternary sequences with optimal balance property and out-of-phase autocorrelation values as{0,-2},{0,2,-2} and {0,-2,-2i,2i} were constructed respectively.Through these constructions,all the almost quaternary sequences constructed are balanced and optimal.These constructed sequences extend the existence range of the balanced optimal quaternary sequences and provide more optimal sequences for practical applications.

Key words: quaternary sequence, optimal almost quaternary sequence, balanced sequence, cyclotomic classes

中图分类号:

TN911.2

彭秀平,冀惠璞,郑德亮,牛晓霞. 周期为2q理想几乎四进制序列构造研究[J]. 通信学报, 2019, 40(12): 105-113.

Xiuping PENG,Huipu JI,Deliang ZHENG,Xiaoxia NIU. Study on the constructions of optimal almost quaternary sequences with period 2q[J]. Journal on Communications, 2019, 40(12): 105-113.

图/表 6

表1

表2

表3

表4

表5

表6

参考文献 14

[1]	沈秀敏 . 基于分圆类的理想序列偶设计[D]. 秦皇岛:燕山大学, 2017: 74-96.
	SHEN X M . The design of optimal sequence pairs based on cyclotomy[D]. Qinhuangdao:Yanshan University, 2017: 74-96.
[2]	SCHOTTEN H D , . New optimum ternary complementary sets and almost quadriphase perfect sequences[C]// International Conference on Neural Networks and Signal Processing. 1995: 1106-1109.
[3]	SCHOTTEN H D , . Optimum complementary sets and quadriphase sequences derived from q-ary m-sequences[C]// IEEE International Symposium on Information Theory. IEEE, 1997:485.
[4]	LüKE H D , SCHOTTEN H D ， HADINEJAD-MAHRAM H . Binary and quadriphase sequences with optimal autocorrelation properties:a survey[J]. IEEE Transactions on Information Theory, 2003,49(12): 3271-3282.
[5]	TANG X H , DING C S . New classes of balanced quaternary and almost balanced binary sequences with optimal autocorrelation value[J]. IEEE Transactions on Information Theory, 2010,56(12): 6398-6405.
[6]	KIM Y S , JANG J W , KIM S H ,et al. New quaternary sequences with optimal autocorrelation[C]// IEEE International Symposium on Information Theory. IEEE, 2009: 286-289.
[7]	JANG J W , KIM Y S , KIM S H ,et al. New quaternary sequences with ideal autocorrelation constructed from binary sequences with ideal autocorrelation[C]// IEEE International Symposium on Information The ory. IEEE, 2009: 278-281.
[8]	KIM Y S , J ANG J W , KIM S H ,et al. New constrruction of quaterna ary sequences with ideal autocorrelation from Legeendre sequences[C]// IEEE Internaational Symposium on Information Theory. IEEE, 2009: 282-285.
[9]	EDEMSKIY V , IVANOV A . Autocorrelation and linear complexity of quaternary seequences of period 2p based on cyclo otomic classes of o order four[C]// /IEEE Internationaal Symposium on Information Theorry. IEEE, 2013: 3120-3124.
[10]	SHEN X M , JIA Y G , WAN G J Q ,et al. New families of balanc ed quaternary seequences of even p period with three-leevel optimal autoco orrelation[J]. IEEE Communicationns Letters, 2017,211(10): 2146-2149.
[11]	TANG X H, , LINDNER J . Almost quadriphase sequence with ideeal autocorrelatioon property[J]. IEEE Signal Processsing Letters, 2009,16(1): 38-40.
[12]	彭秀平 . 二值和三值自相关序列偶设计理论研究[D]. 秦皇岛:燕山大学, 201444: 82-86.
	PENG X P . Research on the design theory of sequence pair wiith two-level and d three-level corre lation[D]. Qinhuanngdao:Yanshan Un niversity, 2014： 82-86.
[13]	STORER T . Cyclotomy and ddifference sets[M]. Chicago: MarkhamPress, 1967: 75-77.
[14]	阮传概, 孙伟 . 近世代数及其应用[M]. 北京: 北京邮电大学出版社, 2001: 163-296.
	RUAN C G , SUN W . Modern algebra and appliication[M]. Beijinng: Beijing Univversity of Posts and Telecommuniccations PressPress, 2001: 163-296.

(i,j)	n≡1(mod 4)	n≡3(mod 4)
16(0,0)	q- 7+2n	q- 7-2n
16(0,1)	q+ 1+2n-8m	q+ 1-2n-8m
16(0,2)	q+ 1-6n	q+ 1+6n
16(0,3)	q+ 1+2n+8m	q+ 1-2n+8m
16(1,0)	q- 3-2n	q- 3+2n

(i,j)	n≡1(mod 4)	n≡3(mod 4)
16(0,0)	q-11-6n	q-11+6n
16(0,1)	q- 3+2n+8m	q- 3-2n+8m
16(0,2)	q- 3+2n	q- 3-2n
16(0,3)	q- 3+2n-8m	q- 3-2n-8m
16(1,2)	q+ 1-2n	q+ 1+2n

(a₀,a₁,a₂,a₃)	(j₀,j₁,j₂,j₃)	(b₀,b₁,b₂,b₃)	(l₀,l₁,l₂,l₃)
(0,1,0,1)	(0,0,1,1)	(0,1,0,1)	(2,2,3,3)
	(0,0,1,2)		(3,1,2,3)
	(0,1,1,0)		(2,3,3,2)
	(0,2,1,0)		(3,3,2,1)
	(0,0,2,1)		(1,3,3,2)
	(0,1,2,0)		(1,2,3,3)
(0,0,0,0)	(0,1,2,3)	(1,1,1,1)	(1,2,3,0)
	(0,1,2,3)		(3,0,1,2)

(a 0,a1,a2,a3)	(j0,j1,j2,j3)	(b 0,b1,b2,b3)	(l 0,l1,l2,l3)
(0,0,0,0)	(0,1,2,3)	(1,1,1,1)	(0,3,2,1)
	(0,1,2,3)		(2,1,0,3)
	(0,3,2,1)		(0,1,2,3)
	(0,3,2,1)		(2,3,0,1)

f	(j 0,j1,j2,j3)	(l 0,l1,l2,l3)	(y(0),y(q))	Ry (δ)
f 为正整数	(0,0,1,1)	(2,2,3,3)	(0,±1)，(±i,0)	R′_y(δ)
	(0,1,1,0)	(2,3,3,2)
f 为偶数	(0,0,1,2)	(3,1,2,3)	(0,±1)，(±i,0)	R′_y(δ)
	(0,2,1,0)	(3,3,2,1)
f 为奇数	(0,0,2,1)	(1,3,3,2)	(±1,0)，(0,±i)	R′_y′ (δ)
	(0,1,2,0)	(1,2,3,3)

周期为2q理想几乎四进制序列构造研究

Study on the constructions of optimal almost quaternary sequences with period 2q

在线阅读

PDF下载

可视化

摘要/Abstract

引用本文

使用本文

图/表 6

参考文献 14

相关文章 1

Metrics

推荐阅读 0

周期N	(几乎)四进制	旁瓣值	Rmax	平衡性	定理
N = 2(2ⁿ-1)	四进制	{0,-2}	2	平衡	逆gray映射^[7]
N = 2q	四进制	{0,-2}	2	平衡	逆gray映射^[8]
N = pⁿ-1	四进制	{2i,-2i,-2}	2	几乎平衡	逆gray映射^[6]
N =2q,q≡3(mod 4)	四进制	{0,-2}	2	平衡	逆gray映射^[5]
N =2q,q≡1(mod 8)	四进制	{0,-2,2,-4}	4	平衡	四阶分圆^[9]
N =2q,q≡5(mod 8)	四进制	{-2,±2i,-2±2i}	8	平衡	四阶分圆^[9]
N=2q,q=4 ²m +1,m 为偶数	四进制	{2,-2}	2	平衡	四阶分圆^[10]
N = 2q,q=4+n²,n 为奇数	四进制	{2,-2}	2	平衡	四阶分圆^[10]
N≡0(mod 4)	几乎四进制	{0,-4}	4	平衡	交织法^[12]
N= 2q,q=4 f +1	几乎四进制	{0,-2}	2	平衡	定理 1,本文
N=2q,q=4 ²m +1,m为奇数	几乎四进制	{0,2,-2}	2	平衡	推论 1,本文
N= 2q,q=4 f +1	几乎四进制	{0,2,-2}	2	平衡	定理 2,本文
N= 2q,q=4 f +1,f 为偶数	几乎四进制	{0,2,-2}	2	平衡	定理 2,本文
N= 2q,q=4 f +1,f 为奇数	几乎四进制	{0,-2,2i,-2i}	2	平衡	定理 2,本文