|
|
|
| Autocorrelation Distribution of Binary Generalized Legendre-Sidelnikov Sequences |
| KE Pinhui① YE Zhifan① CHANG Zuling② |
①(Fujian Provincial Key Laboratory of Network Security and Cryptology, Fuzhou 350117, China)
②(School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China) |
|
|
|
|
Abstract Compared with the original Legendre-Sidelnikov sequence, the generalized Legendre-Sidelnikov sequence has a better balanced property. For its autocorrelation distribution, however, only some special cases are known. In this paper, using the character sums, the autocorrelation distribution of the generalized binary Legendre-Sidelnikov sequence is determined completely. The result shows that the generalized Legendre-Sidelnikov sequence possesses a better autocorrelation distribution if p≡3 (mod 4) and q>>p .
|
|
Received: 08 June 2015
Published: 19 November 2015
|
|
|
| Fund: Fujian Normal University Innovative Research Team (IRTL1207), Natural Science Foundation of Fujian Province (2015J01237), The Joint Funds of the National Natural Science Foundation of China (U1304604) |
|
Corresponding Authors:
KE Pinhui
E-mail: keph@fjnu.edu.cn
|
|
|
|
| [1] |
GOLOMB G and GONG G. Signal Designs with Good Correlations: Forwireless Communications, Cryptography and Radar Applications[M]. Cambridge, U.K.: Cambridge University Press, 2005: 174-175.
|
| [2] |
ARASU K T, DING C, HELLESETH T, et al. Almost difference sets and their sequences with optimal autocorrelation[J]. IEEE Transactions on Information Theory, 2001, 47(7): 2934-2943.
|
| [3] |
陈晓玉, 许成谦, 李玉博. 新的完备高斯整数序列的构造方法[J]. 电子与信息学报, 2014, 36(9): 2081-2085. doi: 10.3724/SP. J.1146.2103.01697.
|
|
CHEN Xiaoyu, XU Chengqian, and LI Yubo. New constructions of perfect Gaussian integer sequences[J]. Journal of Electronics & Information Technology, 2014, 36 (9): 2081-2085. doi: 10.3724/SP.J.1146.2103.01697.
|
| [4] |
李瑞芳, 柯品惠. 一类新的周期为2pq的二元广义分圆序列的线性复杂度[J]. 电子与信息学报, 2014, 36(3): 650-654. doi: 10.3724/SP.J.1146.2103.00751.
|
|
LI Ruifang and KE Pinhui. The linear complexity of a new class of generalized cyclotomic sequence with period 2pq[J]. Journal of Electronics & Information Technology, 2014, 36 (3): 650-654. doi: 10.3724/SP.J.1146.2103.00751.
|
| [5] |
DING C, HELLESETH T, and SAN W. On the linear complexity of Legendre sequences[J]. IEEE Transactions on Information Theory, 1998, 44(3): 1276-1278.
|
| [6] |
DING C. Pattern distributions of Legendre sequences[J]. IEEE Transactions on Information Theory, 1998, 44(4): 1693-1698.
|
| [7] |
SIDELNIKOV V M. Some k-valued pseudo-random sequences and nearly equidistant codes[J]. Problems of Information Transmission, 1969, 5(1): 12-16.
|
| [8] |
岳曌, 高军涛, 谢佳. 双素数Sidel’nikov序列的自相关函数[J]. 电子与信息学报, 2013, 35 (11): 2602-2607. doi: 10.3724/ SP.J.1146.2103.00147.
|
|
YUE Zhao, GAO Juntao, and XIE Jia. Autocorrelation of the two-prime Sidel’nikov sequence[J]. Jounal of Electronics & Information Technology, 2013, 35(11): 2602-2607. doi: 10.3724/SP.J.1146.2103.00147.
|
| [9] |
KIM Youngtae, SONG Minkyu, KIM Daesan, et al. Properties and crosscorrelation of decimated sidelnikov sequences[J]. IEICE Transactions on Fundamentals, 2014,
|
| 97 |
-A(12): 2562-2566.
|
| [10] |
KIM Youngtae, KIM Daesan, and SONG Hongyeop. New M-Ary sequence families with low correlation from the array structure of sidelnikov sequences[J]. IEEE Transactions on Information Theory, 2015, 61(1): 655-670.
|
| [11] |
SU M and WINTERHOF A. Autocorrelation of Legendre- Sidelnikov sequences[J]. IEEE Transactions on Information Theory, 2010, 56(4): 1714-1718.
|
| [12] |
SU M. On the linear complexity of Legendre-Sidelnikov sequences[J]. Design Codes and Cryptography, 2015, 74(3): 703-717.
|
| [13] |
SU M and WINTERHOF A. Correlation measure of order k and linear complexity profile of legendre-sidelnikov sequences[C]. Proceedings of Fifth International Workshop on Signal Design and its Applications in Communications, Guilin, China, 2011: 6-8.
|
| [14] |
SU M. ON the d-ary Generalized Legendre-Sidelnikov Sequence[J]. LNCS, 2012, 7280: 233-244.
|
| [15] |
YAN T, LIU H, and SUN Y. Autocorrelation of modified Legendre-Sidelnikov sequences[J]. IEICE Transactions on Fundamentals, 2015, E98-A(2): 771-775.
|
| [16] |
BURTON D M. Elementary Number Theory[M]. Maidenhead: UK, McGraw-Hill Education Press, 1998: 92-105.
|
| [17] |
LIDL R and NIEDERREITER H. Finite Fields[M]. MA: Addision-Wesley, 1983: 217-225.
|
|
|
|
