Linear Complexity over Fq of a Class of Generalized Cyclotomic Quaternary Sequences with Period 2p2

Yan WANG; Naijiao XIANG; Xilin HAN; Liantao YAN

doi:10.11999/JEIT210095

Volume 43 Issue 10

Oct. 2021

Turn off MathJax

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2021 > 43(10): 2936-2943

Yan WANG, Naijiao XIANG, Xilin HAN, Liantao YAN. Linear Complexity over Fq of a Class of Generalized Cyclotomic Quaternary Sequences with Period 2p2[J]. Journal of Electronics & Information Technology, 2021, 43(10): 2936-2943. doi: 10.11999/JEIT210095

Citation:

Yan WANG, Naijiao XIANG, Xilin HAN, Liantao YAN. Linear Complexity over F_q of a Class of Generalized Cyclotomic Quaternary Sequences with Period 2p²[J]. Journal of Electronics & Information Technology, 2021, 43(10): 2936-2943. doi: 10.11999/JEIT210095

Citation:

PDF( 571 KB)

Linear Complexity over F_q of a Class of Generalized Cyclotomic Quaternary Sequences with Period 2p²

doi: 10.11999/JEIT210095

School of Science, Xi’ an University of Architecture and Technology, Xi’an 710055, China

Funds: The National Natural Science Foundation of China (61902304), and The Project Supported by Natural Science Basic Research Plan in Shaanxi Province of China (2021JQ-495)

Received Date: 2021-01-26
Rev Recd Date: 2021-07-16

Available Online: 2021-07-29

Publish Date: 2021-10-18

Abstract

Abstract

Based on the theory of generalized cyclotomy, the minimal polynomial and linear complexity of a class of generalized cyclotomic quaternary sequences with period $2{p^2}$ are determined by explicitly computing the number of zeros of the generating polynomial over ${F_q}$($q = {r^m}$). The results show that the linear complexity is more than ${p^2}$, the half of the period $2{p^2}$. According to Berlekamp-Massey algorithm, these sequences can be viewed as enough good for the utilizing in cryptography.
- Generalized cyclotomic sequences,
- Quaternary sequences,
- Linear complexity,
- Generating polynomial,
- Minimal polynomial

FullText(HTML)

References(15)

References

[1]	GOLOMB S W and GONG Guang. Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar[M]. Cambridge: Cambridge University Press, 2005: 174–175.
[2]	DING Cunsheng. Linear complexity of generalized cyclotomic binary sequences of order 2[J]. Finite Fields and Their Applications, 1997, 3(2): 159–174. doi: 10.1006/ffta.1997.0181
[3]	BAI Enjian, LIU Xiaojuan, and XIAO Guozhen. Linear complexity of new generalized cyclotomic sequences of order two of length pq[J]. IEEE Transactions on Information Theory, 2005, 51(5): 1849–1853. doi: 10.1109/TIT.2005.846450
[4]	李胜强, 周亮, 肖国镇. 一类周期为pq阶为2的Whiteman广义分圆序列研究[J]. 电子与信息学报, 2009, 31(9): 2205–2208. LI Shengqiang, ZHOU Liang, and XIAO Guozhen. Study on a class of Whiteman-Generalized cyclotomic sequence with length pq and order two[J]. Journal of Electronics &Information Technology, 2009, 31(9): 2205–2208.
[5]	XIAO Zibi, ZENG Xiangyong, LI Chunlei, et al. New generalized cyclotomic binary sequences of period p²[J]. Designs, Codes and Cryptography, 2018, 86(7): 1483–1497. doi: 10.1007/s10623-017-0408-7
[6]	EDEMSKIY V, LI Chunlei, ZENG Xiangyong, et al. The linear complexity of generalized cyclotomic binary sequences of period p ⁿ[J]. Designs, Codes and Cryptography, 2019, 87(5): 1183–1197. doi: 10.1007/s10623-018-0513-2
[7]	OUYANG Yi and XIE Xianhong. Linear complexity of generalized cyclotomic sequences of period 2p ^m[J]. Designs, Codes and Cryptography, 2019, 87(11): 2585–2596. doi: 10.1007/s10623-019-00638-5
[8]	王艳, 薛改娜, 李顺波, 等. 一类新的周期为2p ^m的q阶二元广义分圆序列的线性复杂度[J]. 电子与信息学报, 2019, 41(9): 2151–2155. doi: 10.11999/JEIT180884 WANG Yan, XUE Gaina, LI Shunbo, et al. The linear complexity of a new class of generalized cyclotomic sequence of order q with period 2p ^m[J]. Journal of Electronics &Information Technology, 2019, 41(9): 2151–2155. doi: 10.11999/JEIT180884
[9]	WANG Qiuyan, WU Chenhuang, YANG Minghui, et al. A kind of quaternary sequences of period 2p^mqⁿ and their linear complexity[J]. arXiv preprint arXiv: 2001.10839, 2020.
[10]	KE Pinhui, ZHONG Yan, and ZHANG Shengyuan. Linear complexity of a new class of quaternary generalized cyclotomic sequence with period 2p ^m[J]. Complexity, 2020, 2020: 6538970. doi: 10.1155/2020/6538970
[11]	DU Xiaoni and CHEN Zhixiong. Linear complexity of quaternary sequences generated using generalized cyclotomic classes modulo 2p[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2011, E94-A(5): 1214–1217. doi: 10.1587/transfun.E94.A.1214
[12]	CHEN Zhixiong and EDEMSKIY V. Linear complexity of quaternary sequences over Z₄ derived from generalized cyclotomic classes modulo 2p[J]. arXiv preprint arXiv: 1603.05086, 2016.
[13]	杜小妮, 赵丽萍, 王莲花. Z₄上周期为2p²的四元广义分圆序列的线性复杂度[J]. 电子与信息学报, 2018, 40(12): 2992–2997. doi: 10.11999/JEIT180189 DU Xiaoni, ZHAO Liping, and WANG Lianhua. Linear complexity of quaternary sequences over Z₄ derived from generalized cyclotomic classes modulo 2p²[J]. Journal of Electronics &Information Technology, 2018, 40(12): 2992–2997. doi: 10.11999/JEIT180189
[14]	ZHANG Jingwei, ZHAO Changan, and MA Xiao. On the linear complexity of generalized cyclotomic binary sequences with length 2p²[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2010, E93-A(1): 302–308. doi: 10.1587/transfun.E93.A.302
[15]	DING Cunsheng and HELLESETH T. New generalized cyclotomy and its applications[J]. Finite Fields and Their Applications, 1998, 4(2): 140–166. doi: 10.1006/ffta.1998.0207