A New Class of Binary Sequence Family with Low Correlation and Large Linear Complexity

2007 ◽  
Author(s):  
Jin-Song Wang ◽  
Wen-Feng Qi
Keyword(s):  
Linear Complexity ◽  
Binary Sequence ◽  
Sequence Family ◽  
New Class ◽  
Low Correlation

A new class of quaternary generalized cyclotomic sequences of order 2d and length 2pm with high linear complexity

2018 ◽  
Vol 16 (01) ◽  
pp. 1850006 ◽  
Author(s):  
Longfei Liu ◽  
Xiaoyuan Yang ◽  
Bin Wei ◽  
Liqiang Wu
Keyword(s):  
Finite Fields ◽  
Linear Complexity ◽  
Periodic Sequences ◽  
New Class ◽  
New Family ◽  
Generalized Cyclotomic Classes ◽  
Cyclotomic Sequences

Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudo-random properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. In this paper, we construct a new family of quaternary generalized cyclotomic sequences with order [Formula: see text] and length [Formula: see text], which generalize the sequences constructed by Ke et al. in 2012. In addition, we determine its linear complexity using cyclotomic theory. The conclusions reveal that these sequences have high linear complexity, which means they can resist linear attacks.

A Class of Large Family of Binary Sequences with Low Correlation and Large Linear Span

2013 ◽  
Vol 385-386 ◽  
pp. 1562-1567
Author(s):  
Jun Chen ◽  
Yun Chen
Keyword(s):  
Linear Span ◽  
Large Family ◽  
Binary Sequences ◽  
Sequence Family ◽  
New Family ◽  
Low Correlation

In this paper, a new family of binary sequences of period is proposed, where and . The presented family takes 7-valued correlation values , , , , , and . For and , it is proved that the proposed sequence family has linear spans , where l = 2, 3, 4, 5, 6, 7, and the distribution of linear span of sequences in is determined.

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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