scholarly journals Linear Complexity of Periodically Repeated Random Sequences

2007 ◽  
pp. 168-175 ◽  
Author(s):  
Zong-Duo Dai ◽  
Jun-Hui Yang
Keyword(s):  
Linear Complexity ◽  
Random Sequences

scholarly journals New Generalized Cyclotomic Quaternary Sequences with Large Linear Complexity and a Product of Two Primes Period

Information ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 193
Author(s):  
Jiang Ma ◽  
Wei Zhao ◽  
Yanguo Jia ◽  
Haiyang Jiang
Keyword(s):  
Spectral Sequence ◽  
Linear Complexity ◽  
Residue Class ◽  
Important Criterion ◽  
Random Sequences ◽  
Gray Mapping ◽  
Quaternary Sequences ◽  
Hamming Weights ◽  
Residue Class Ring ◽  
Class Ring

Linear complexity is an important criterion to characterize the unpredictability of pseudo-random sequences, and large linear complexity corresponds to high cryptographic strength. Pseudo-random Sequences with a large linear complexity property are of importance in many domains. In this paper, based on the theory of inverse Gray mapping, two classes of new generalized cyclotomic quaternary sequences with period pq are constructed, where pq is a product of two large distinct primes. In addition, we give the linear complexity over the residue class ring Z4 via the Hamming weights of their Fourier spectral sequence. The results show that these two kinds of sequences have large linear complexity.

2-Adic and Linear Complexities of a Class of Whiteman’s Generalized Cyclotomic Sequences of Order Four

2019 ◽  
Vol 30 (05) ◽  
pp. 759-779
Author(s):  
Priti Kumari ◽  
Pramod Kumar Kewat
Keyword(s):  
Linear Complexity ◽  
Binary Sequences ◽  
Random Sequences ◽  
Generalized Cyclotomic Classes ◽  
Order Four ◽  
Cyclotomic Sequences

Although for more than 20 years, Whiteman’s generalized cyclotomic sequences have been thought of as the most important pseudo-random sequences, but, there are only a few papers in which their 2-adic complexities have been discussed. In this paper, we construct a class of binary sequences of order four with odd length (product of two distinct odd primes) from Whiteman’s generalized cyclotomic classes. After that, we determine both 2-adic complexity and linear complexity of these sequences. Our results show that these complexities are greater than half of the period of the sequences, therefore, it may be good pseudo-random sequences.

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.

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