The linear complexity of balanced quaternary sequences with optimal autocorrelation value

2015 ◽  
Vol 7 (4) ◽  
pp. 485-496 ◽  
Author(s):  
Vladimir Edemskiy ◽  
Andrey Ivanov
Keyword(s):  
Linear Complexity ◽  
Quaternary Sequences ◽  
Autocorrelation Value

scholarly journals Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yan Wang ◽  
Liantao Yan ◽  
Qing Tian ◽  
Liping Ding
Keyword(s):  
Autocorrelation Function ◽  
Linear Complexity ◽  
Minimal Polynomial ◽  
Binary Sequences ◽  
Cyclotomic Class ◽  
Cyclotomic Sequences ◽  
Autocorrelation Value

Ding constructed a new cyclotomic class V 0   , V 1 . Based on it, a construction of generalized cyclotomic binary sequences with period p q is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function C S w is 3-level if p ≡ 3 mod 4 , and C S w is 5-level if p ≡ 1 mod 4 . The linear complexity LC S > p q / 2 if p ≡ 1   mod   8 , p > q + 1 , or p ≡ 3 mod 4 or p ≡ − 3 mod 8 . The results show that these sequences have quite good cryptographic properties in the aspect of autocorrelation and linear complexity.

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.

Linear complexity of generalised cyclotomic quaternary sequences of length 2p m+1 q n+1

2016 ◽  
Vol 10 (2) ◽  
pp. 104-111
Author(s):  
Dan-dan Li ◽  
Qiao-yan Wen ◽  
Zu-ling Chang ◽  
Jie Zhang
Keyword(s):  
Linear Complexity ◽  
Quaternary Sequences

scholarly journals Linear Complexity over Fq of Generalized Cyclotomic Quaternary Sequences with Period 2p

2015 ◽  
Vol E98.A (7) ◽  
pp. 1569-1575 ◽  
Author(s):  
Minglong QI ◽  
Shengwu XIONG ◽  
Jingling YUAN ◽  
Wenbi RAO ◽  
Luo ZHONG
Keyword(s):  
Linear Complexity ◽  
Quaternary Sequences ◽  
Period 2
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