scholarly journals The linear complexity of new q-ary generalized cyclotomic sequences of period pn

2019 ◽  
Vol 292 ◽  
pp. 02001
Author(s):  
Vladimir Edemskiy ◽  
Nikita Sokolovskiy
Keyword(s):  
Finite Field ◽  
Linear Complexity ◽  
Cyclotomic Sequences

In this paper, we study the linear complexity of new q-ary generalized cyclotomic sequences of length pn over the finite field of order q. We show that these sequences have the high linear complexity when n ≥ 2. These sequences are constructed by new generalized cyclotomic classed prepared by X. Zeng at el.

scholarly journals Linear Complexity of Generalized Cyclotomic Sequences of Order 4 over Fl

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Yuhua Sun ◽  
Qiuyan Wang ◽  
Yang Yan ◽  
Tongjiang Yan ◽  
Hui Li
Keyword(s):  
Finite Field ◽  
Linear Complexity ◽  
Cyclotomic Sequences

Generalized cyclotomic sequences of period pq have several desirable randomness properties if the two primes p and q are chosen properly. In particular, Ding deduced the exact formulas for the autocorrelation and the linear complexity of these sequences of order 2. In this paper, we consider the generalized sequences of order 4. Under certain conditions, the linear complexity of these sequences is developed over a finite field Fl. The results show that, in many cases, they have high linear complexity.

scholarly journals Linear Complexity of a New Class of Quaternary Generalized Cyclotomic Sequence with Period 2pm

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Pinhui Ke ◽  
Yan Zhong ◽  
Shengyuan Zhang
Keyword(s):  
Finite Field ◽  
Linear Complexity ◽  
Generalized Cyclotomy ◽  
New Class ◽  
Generalized Cyclotomic Sequence ◽  
Cyclotomic Sequences

Sequences with high linear complexity property are of importance in applications. In this paper, based on the theory of generalized cyclotomy, new classes of quaternary generalized cyclotomic sequences with order 4 and period 2pm are constructed. In addition, we determine their linear complexities over finite field F4 and over ℤ4, respectively.

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.

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.

Autocorrelation values of quaternary cyclotomic sequence of length 2pm

2020 ◽  
Vol 18 (06) ◽  
pp. 2050047
Author(s):  
Huaning Liu ◽  
Xiaolin Chen
Keyword(s):  
Linear Complexity ◽  
Cyclotomic Sequences

We completely determine the autocorrelations of the quaternary cyclotomic sequences over [Formula: see text] of length [Formula: see text] presented in [P. Ke and S. Zhang, New classes of quaternary cyclotomic sequence of length [Formula: see text] with high linear complexity, Inf. Process. Lett. 112 (2012) 646–650] in general without the restrictions about [Formula: see text].

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