Construction of Binary Sequences With Low Correlation via Multiplicative Quadratic Character Over Finite Fields of Odd Characteristics

被引：2
作者：
Jin, Lingfei [1 ,2 ,3 ]
Chen, Dawei [4 ]
Qian, Luyan [1 ,2 ,3 ]
Teng, Jiaming [1 ,2 ,3 ]
Chen, Shijun [4 ]
机构：
[1] Fudan Univ, Sch Comp Sci, Shanghai Key Lab Intelligent Informat Proc, Shanghai 200433, Peoples R China
[2] Shanghai Engn Res Ctr Blockchain, Fudan Zhongan Joint Lab Blockchain & Informat Sec, Shanghai 200433, Peoples R China
[3] Shanghai Inst Intelligent Elect & Syst, Shanghai 200433, Peoples R China
[4] ZTE Corp, Shenzhen 518057, Peoples R China
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2021年 / 67卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Gold sequences; binary sequences; finite fields; multiplicative quadratic character;
D O I：
10.1109/TIT.2021.3059041
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In literature, there are several methods to construct Gold sequences. One of the constructions is via the trace function from extension field of F-2. Estimation of correlation of this construction is based on number of rational points of elliptic curves. In this article, we generalize this construction from finite fields of even characteristic to odd characteristics by using multiplicative quadratic character. Again, estimation of correlation of this construction is based on number of rational points of elliptic curves. Thus, we obtain binary sequences which have more flexibility on length while still possessing low correlation property. Moreover, some of the sequences are optimally balanced.
引用
收藏
页码：2236 / 2244
页数：9
相关论文
共 22 条
[1]   BINARY SEQUENCES WITH GOLD-LIKE CORRELATION BUT LARGER LINEAR SPAN [J].
BOZTAS, S ;
KUMAR, PV .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1994, 40 (02) :532-537
[2]  
Golomb SW., 1967, SHIFT REGISTER SEQUE
[3]  
JENSEN HE, 1989, LECT NOTES COMPUT SC, V356, P306
[4]  
Kasami T., 1996, COORDINATED SIENCE L
[5]   New families of binary sequences with low correlation [J].
Kim, SH ;
No, JS .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (11) :3059-3065
[6]   D-FORM SEQUENCES - FAMILIES OF SEQUENCES WITH LOW CORRELATION VALUES AND LARGE LINEAR SPANS [J].
KLAPPER, AM .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1995, 41 (02) :423-431
[7]   CLASS OF BALANCED BINARY SEQUENCES WITH OPTIMAL AUTOCORRELATION PROPERTIES [J].
LEMPEL, A ;
COHN, M ;
EASTMAN, WL .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1977, 23 (01) :38-42
[8]   Integrating GPS trajectory and topics from Twitter stream for human mobility estimation [J].
Miyazawa, Satoshi ;
Song, Xuan ;
Xia, Tianqi ;
Shibasaki, Ryosuke ;
Kaneda, Hodaka .
FRONTIERS OF COMPUTER SCIENCE, 2019, 13 (03) :460-470
[9]   Trace representation of Legendre sequences of Mersenne prime period [J].
No, JS ;
Lee, HK ;
Chung, HB ;
Song, HY ;
Yang, K .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1996, 42 (06) :2254-2255
[10]   A NEW FAMILY OF BINARY PSEUDORANDOM SEQUENCES HAVING OPTIMAL PERIODIC CORRELATION-PROPERTIES AND LARGE LINEAR SPAN [J].
NO, JS ;
KUMAR, PV .
IEEE TRANSACTIONS ON INFORMATION THEORY, 1989, 35 (02) :371-379
123