Computing the error linear complexity spectrum of a binary sequence of period 2/sup n/

2003 ◽  
Vol 49 (1) ◽  
pp. 273-280 ◽  
Author(s):  
A.G.B. Lauder ◽  
K.G. Paterson
Keyword(s):  
Linear Complexity ◽  
Binary Sequence ◽  
Period 2 ◽  
Error Linear Complexity ◽  
Error Linear Complexity Spectrum

An Efficient Algorithm for Computing the k-Error Linear Complexity Spectrum of Periodic Sequences

2012 ◽  
Vol 532-533 ◽  
pp. 1726-1731
Author(s):  
Ling Yong Ma ◽  
Hao Cao
Keyword(s):  
Efficient Algorithm ◽  
Linear Complexity ◽  
Primitive Root ◽  
Periodic Sequences ◽  
Period 2 ◽  
Primitive Root Modulo ◽  
Modulo P ◽  
Error Linear Complexity ◽  
Error Linear Complexity Spectrum

An efficient algorithm for computing the k-error linear complexity spectrum of a q- ary sequence s with period 2 pn is presented, where q is an odd prime and a primitive root modulo p2. The algorithm generalizes both the Wei-Xiao-Chen and the Wei algorithms, The new algorithm can compute the k-error linear complexity spectrum of s using at most 4 n+1 steps.

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.

Properties of the Error Linear Complexity Spectrum

2009 ◽  
Vol 55 (10) ◽  
pp. 4681-4686 ◽  
Author(s):  
Tuvi Etzion ◽  
Nicholas Kalouptsidis ◽  
Nicholas Kolokotronis ◽  
Konstantinos Limniotis ◽  
Kenneth G. Paterson
Keyword(s):  
Linear Complexity ◽  
Error Linear Complexity ◽  
Error Linear Complexity Spectrum

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.

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