scholarly journals Linear Complexity of the Balanced Polynomial Quotients Sequences

2018 ◽  
Vol 228 ◽  
pp. 01014
Author(s):  
Chun-e Zhao ◽  
Tongjiang Yan ◽  
Qihua Niu
Keyword(s):  
Lower Bound ◽  
Communication Systems ◽  
Linear Complexity ◽  
Binary Sequences ◽  
The Past ◽  
Error Linear Complexity

Balanced binary sequences of large linear complexity have series applications in communication systems. In the past, although the sequences derived from polynomial quotients have large linear complexity, but they are not balanced. In this paper, we will construct new sequences which are not only with large linear complexity but also balanced. Meanwhile, this linear complexity reaches the known k-error linear complexity mentioned in [7], which means that the k-error linear complexity as a lower bound is tight.

scholarly journals On the k-Error Linear Complexity of Binary Sequences Derived from the Discrete Logarithm in Finite Fields

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Zhixiong Chen ◽  
Qiuyan Wang
Keyword(s):  
Lower Bound ◽  
Finite Field ◽  
Finite Fields ◽  
Linear Complexity ◽  
Discrete Logarithm ◽  
Binary Sequence ◽  
Binary Sequences ◽  
Quadratic Character ◽  
Legendre Sequence ◽  
Error Linear Complexity

Let Fq be the finite field with q=pr elements, where p is an odd prime. For the ordered elements ξ0,ξ1,…,ξq-1∈Fq, the binary sequence σ=(σ0,σ1,…,σq-1) with period q is defined over the finite field F2={0,1} as follows: σn=0,  if  n=0,  (1-χ(ξn))/2,  if  1≤n<q,  σn+q=σn, where χ is the quadratic character of Fq. Obviously, σ is the Legendre sequence if r=1. In this paper, our first contribution is to prove a lower bound on the linear complexity of σ for r≥2, which improves some results of Meidl and Winterhof. Our second contribution is to study the distribution of the k-error linear complexity of σ for r=2. Unfortunately, the method presented in this paper seems not suitable for the case r>2 and we leave it open.

scholarly journals On $k$-error linear complexity of pseudorandom binary sequences derived from Euler quotients

2018 ◽  
Vol 12 (4) ◽  
pp. 805-816 ◽  
Author(s):  
Zhixiong Chen ◽  
◽  
Vladimir Edemskiy ◽  
Pinhui Ke ◽  
Chenhuang Wu ◽  
...  
Keyword(s):  
Linear Complexity ◽  
Binary Sequences ◽  
Error Linear Complexity

ON THE -ERROR LINEAR COMPLEXITY OF SEQUENCES FROM FUNCTION FIELDS

2020 ◽  
Vol 102 (2) ◽  
pp. 342-352
Author(s):  
YUHUI ZHOU ◽  
YUHUI HAN ◽  
YANG DING
Keyword(s):  
Lower Bound ◽  
Linear Complexity ◽  
Function Fields ◽  
Stream Ciphers ◽  
Security Measures ◽  
Periodic Sequences ◽  
Error Linear Complexity

The linear complexity and the error linear complexity are two important security measures for stream ciphers. We construct periodic sequences from function fields and show that the error linear complexity of these periodic sequences is large. We also give a lower bound for the error linear complexity of a class of nonperiodic sequences.

On the k-error linear complexity of 2p2-periodic binary sequences

2020 ◽  
Vol 63 (9) ◽  
Author(s):  
Zhihua Niu ◽  
Can Yuan ◽  
Zhixiong Chen ◽  
Xiaoni Du ◽  
Tao Zhang
Keyword(s):  
Linear Complexity ◽  
Binary Sequences ◽  
Error Linear Complexity

scholarly journals On the stability of periodic binary sequences with zone restriction

2020 ◽  
Author(s):  
Ming Su ◽  
Qiang Wang
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Linear Complexity ◽  
Binary Sequence ◽  
Search Space ◽  
Binary Sequences ◽  
Zone Length ◽  
Stability Measure ◽  
Error Linear Complexity ◽  
The Stability

Abstract Traditional global stability measure for sequences is hard to determine because of large search space. We propose the k-error linear complexity with a zone restriction for measuring the local stability of sequences. For several classes of sequences, we demonstrate that the k-error linear complexity is identical to the k-error linear complexity within a zone, while the length of a zone is much smaller than the whole period when the k-error linear complexity is large. These sequences have periods $$2^n$$ 2 n , or $$2^v r$$ 2 v r (r odd prime and 2 is primitive modulo r), or $$2^v p_1^{s_1} \cdots p_n^{s_n}$$ 2 v p 1 s 1 ⋯ p n s n ($$p_i$$ p i is an odd prime and 2 is primitive modulo $$p_i^2$$ p i 2 , where $$1\le i \le n$$ 1 ≤ i ≤ n ) respectively. In particular, we completely determine the spectrum of 1-error linear complexity with any zone length for an arbitrary $$2^n$$ 2 n -periodic binary sequence.

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