长度为奇素数的完备高斯整数序列构造法

doi:10.11959/j.issn.1000-436x.2018230

通信学报 ›› 2018, Vol. 39 ›› Issue (11): 190-197.doi: 10.11959/j.issn.1000-436x.2018230

长度为奇素数的完备高斯整数序列构造法

李玉博^1,²(),陈邈^1,²,刘涛^1,²,张颖^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:2018-09-26 出版日期:2018-11-01 发布日期:2018-12-10
作者简介:李玉博（1985?），男，河北衡水人，博士，燕山大学讲师，主要研究方向为编码理论、序列设计、信息处理。|陈邈（1993?），男，河北唐山人，燕山大学硕士生，主要研究方向为无线通信、序列设计。|刘涛（1987?），女，河北秦皇岛人，燕山大学博士生，主要研究方向为组合编码、信息安全、序列设计。|张颖（1997?），女，山西平定县人，本科生，主要研究方向为无线通信、编码理论。
基金资助:
国家自然科学基金资助项目(61501395)

Constructions of perfect Gaussian integer sequences of odd prime length

Yubo LI^1,²(),Miao CHEN^1,²,Tao LIU^1,²,Ying ZHANG^1,²

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

Revised:2018-09-26 Online:2018-11-01 Published:2018-12-10
Supported by:
The National Natural Science Foundation of China(61501395)

摘要/Abstract

摘要：

提出一类基于分圆类构造完备高斯整数序列的方法。分别通过有限域GF(p)上的2阶和4阶分圆类，构造得到自由度分别为3和5的高斯整数序列，序列长度为奇素数，该序列具有良好的完备自相关性能。该构造方法解决了以往利用分圆类计算复杂度较高，不易求解的问题，简化了序列的生成方法。该序列在无线通信中具有良好的应用前景。

关键词: 完备高斯整数序列, 伪随机序列, 分圆类, 离散傅里叶变换

Abstract:

Constructions of perfect Gaussian integer sequences (PGIS) based on the cyclotomic classes were proposed.The PGIS with degree 3 and 5 were constructed respectively from the cyclotomic classes of order 2 and 4.The presented sequences with odd prime length have ideal autocorrelations.The methods solved the problem that the traditional constructions of PGIS from the cyclotomic classes have high computational complexity.As a result,this kind of sequences will be useful in the applications of wireless communications.

Key words: perfect Gaussian integer sequence, pseudo-random sequence, cyclotomic classes, discrete Fourier transform

中图分类号:

TN911.2

李玉博,陈邈,刘涛,张颖. 长度为奇素数的完备高斯整数序列构造法[J]. 通信学报, 2018, 39(11): 190-197.

Yubo LI,Miao CHEN,Tao LIU,Ying ZHANG. Constructions of perfect Gaussian integer sequences of odd prime length[J]. Journal on Communications, 2018, 39(11): 190-197.

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参考文献 19

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自由度为3的完备高斯整数序列			自由度为5阶完备高斯整数序列
f	p= 2f +1	(a,b)	f	p= 4f +1	(a,b)
2	5	(±1,±2)(±2,±1)	1	5	(±1,±2)(±2,±1)
3	7	不存在	3	13	(±3,±2)(±2,±3)
5	11	不存在	4	17	(±1,±4)(±4,±1)
6	13	(±3,±2)(±2,±3)	7	29	(±2,±5)(±5,±2)
8	17	(±1,±4)(±4,±1)	9	37	(±1,±6)(±6,±1)
9	19	不存在	10	41	(±4,±5)(±5,±4)
11	23	不存在	13	53	(±2,±7)(±7,±2)
14	29	(±2,±5)(±5,±2)	15	61	(±6,±5)(±5,±6)
15	31	不存在	18	73	(±8,±3)(±3,±8)
18	37	(±1,±6)(±6,±1)	22	89	(±8,±5)(±5,±8)
20	41	(±4,±5)(±5,±4)	24	97	(±4,±9)(±9,±4)
21	43	不存在	25	101	(±1,±10)(±10,±1)
23	47	不存在	27	109	(±3,±10)(±10,±3)

长度为奇素数的完备高斯整数序列构造法

Constructions of perfect Gaussian integer sequences of odd prime length

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(j,k)₄	0	1	2	3
0	A	B	C	D
1	E	E	D	B
2	A	E	A	E
3	E	D	B	E

(j,k)₄	0	1	2	3
0	A	B	C	D
1	B	D	E	E
2	C	E	C	E
3	D	E	E	B