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.

2-Adic and Linear Complexities of a Class of Whiteman’s Generalized Cyclotomic Sequences of Order Four

2019 ◽  
Vol 30 (05) ◽  
pp. 759-779
Author(s):  
Priti Kumari ◽  
Pramod Kumar Kewat
Keyword(s):  
Linear Complexity ◽  
Binary Sequences ◽  
Random Sequences ◽  
Generalized Cyclotomic Classes ◽  
Order Four ◽  
Cyclotomic Sequences

Although for more than 20 years, Whiteman’s generalized cyclotomic sequences have been thought of as the most important pseudo-random sequences, but, there are only a few papers in which their 2-adic complexities have been discussed. In this paper, we construct a class of binary sequences of order four with odd length (product of two distinct odd primes) from Whiteman’s generalized cyclotomic classes. After that, we determine both 2-adic complexity and linear complexity of these sequences. Our results show that these complexities are greater than half of the period of the sequences, therefore, it may be good pseudo-random sequences.

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 A Kind of Quaternary Sequences of Period 2pmqn and Their Linear Complexity

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Qiuyan Wang ◽  
Chenhuang Wu ◽  
Minghui Yang ◽  
Yang Yan
Keyword(s):  
Linear Complexity ◽  
New Class ◽  
Quaternary Sequences ◽  
Generalized Cyclotomic Classes

Sequences with high linear complexity have wide applications in cryptography. In this paper, a new class of quaternary sequences over F4 with period 2pmqn is constructed using generalized cyclotomic classes. Results show that the linear complexity of these sequences attains the maximum.

scholarly journals Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 908
Author(s):  
Perla Celis ◽  
Rolando de la Cruz ◽  
Claudio Fuentes ◽  
Héctor W. Gómez
Keyword(s):  
Survival Data ◽  
Maximum Likelihood Estimates ◽  
New Class ◽  
New Family ◽  
Gamma Distributions ◽  
Special Cases ◽  
Log Normal ◽  
Positive Support ◽  
Positive Distributions ◽  
Family Of Distributions

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

scholarly journals Expansion complexity and linear complexity of sequences over finite fields

2016 ◽  
Vol 9 (4) ◽  
pp. 501-509 ◽  
Author(s):  
László Mérai ◽  
Harald Niederreiter ◽  
Arne Winterhof
Keyword(s):  
Finite Fields ◽  
Linear Complexity

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 Constructions of Asymptotically Optimal Codebooks via Cyclotomic Classes of Order 8

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Wanfeng Qi ◽  
Yueying Song ◽  
Rui Ma ◽  
Lingli Tang ◽  
Qian Wang
Keyword(s):  
Finite Fields ◽  
Difference Sets ◽  
Good Alternative ◽  
Asymptotically Optimal ◽  
Welch Bound ◽  
New Class ◽  
Almost Difference Sets

Asymptotically optimal codebooks are a family of codebooks that can approach an optimal codebook meeting the Welch bound when the lengths of codewords are large enough. They can be constructed easily and are a good alternative for optimal codebooks in many applications. In this paper, we construct a new class of asymptotically optimal codebooks by using the product of some special finite fields and almost difference sets, which are composed of cyclotomic classes of order eight.

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