Trace Representation and Linear Complexity of Binary $e$th Power Residue Sequences of Period $p$

2011 ◽  
Vol 57 (3) ◽  
pp. 1530-1547 ◽  
Author(s):  
Zongduo Dai ◽  
Guang Gong ◽  
Hong-Yeop Song ◽  
Dingfeng Ye
Keyword(s):  
Linear Complexity ◽  
Trace Representation

scholarly journals Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2285
Author(s):  
Jiang Ma ◽  
Wei Zhao ◽  
Yanguo Jia ◽  
Xiumin Shen ◽  
Haiyang Jiang
Keyword(s):  
Linear Complexity ◽  
Minimal Polynomial ◽  
Binary Sequences ◽  
Characteristic Set ◽  
Random Sequences ◽  
Generalized Cyclotomy ◽  
Trace Representation ◽  
Cyclotomic Sequences

Linear complexity is an important property to measure the unpredictability of pseudo-random sequences. Trace representation is helpful for analyzing cryptography properties of pseudo-random sequences. In this paper, a class of new Ding generalized cyclotomic binary sequences of order two with period pq is constructed based on the new segmentation of Ding Helleseth generalized cyclotomy. Firstly, the linear complexity and minimal polynomial of the sequences are investigated. Then, their trace representation is given. It is proved that the sequences have larger linear complexity and can resist the attack of the Berlekamp–Massey algorithm. This paper also confirms that generalized cyclotomic sequences with good randomness may be obtained by modifying the characteristic set of generalized cyclotomy.

A Simpler Trace Representation of Legendre Sequences

2015 ◽  
Vol E98.A (4) ◽  
pp. 1026-1031 ◽  
Author(s):  
Minglong QI ◽  
Shengwu XIONG ◽  
Jingling YUAN ◽  
Wenbi RAO ◽  
Luo ZHONG
Keyword(s):  
Trace Representation
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