Autocorrelation and linear complexity of binary generalized cyclotomic sequences with period \(pq\)
type: Item
instance of: scholarly article
title: Autocorrelation and linear complexity of binary generalized cyclotomic sequences with period \(pq\)
zbMATH Open document ID: 1477.94047
DOI: 10.1155/2021/5535887
author: Yan Wang
author: Liantao Yan
author: Qing Tian
author: Liping Ding
published in: Journal of Mathematics
publication date: 2021-06-28T00:00:00Z
review text: Summary: Ding constructed a new cyclotomic class \((V_0, V_1)\). Based on it, a construction of generalized cyclotomic binary sequences with period \(pq\) is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function \(C_S(w)\) is 3-level if \(p\equiv 3\mod 4\), and \(C_S(w)\) is 5-level if \(p\equiv 1\mod 4\). The linear complexity \(\text{LC}( S)>(pq,/,2)\) if \(p\equiv 1\mod 8\), \(p>q+1\), or \(p\equiv 3\mod 4\) or \(p\equiv -3\mod 8\). The results show that these sequences have quite good cryptographic properties in the aspect of autocorrelation and linear complexity.
Mathematics Subject Classification ID: 94A55
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 7363793
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5535887
OpenAlex ID: W3158528406
cites work: A family of difference sets
cites work: New generalized cyclotomy and its applications
cites work: Q5752488
cites work: Q4400352
cites work: On the linear complexity of Hall's sextic residue sequences
cites work: Linear complexity of generalized cyclotomic binary sequences of order 2
cites work: Autocorrelation values of generalized cyclotomic sequences of order two
cites work: Linear complexity of binary Whiteman generalized cyclotomic sequences of order \(2^k\)
cites work: Linear Complexity of New Generalized Cyclotomic Sequences of Order Two of Length&lt;tex&gt;$pq$&lt;/tex&gt;
cites work: On the linear complexity of generalized cyclotomic sequences with the period \(p^m\)
cites work: About computation of the linear complexity of generalized cyclotomic sequences with period \(p^{n+1}\)
cites work: Linear complexity of generalized cyclotomic binary sequences of length \(2p^{m}\)
cites work: The Linear Complexity of Whiteman's Generalized Cyclotomic Sequences of Period $p^{m+1}q^{n+1}$
cites work: On the linear complexity and the autocorrelation of generalized cyclotomic binary sequences of length \(2p^m\)
cites work: Cyclotomic Constructions of Cyclic Codes With Length Being the Product of Two Primes
cites work: Q5193632
cites work: Q4379555
Recommended article: On the linear complexity and autocorrelation of generalized cyclotomic binary sequences with period \(4p^n \)
Recommended article: On the linear complexity and the autocorrelation of generalized cyclotomic binary sequences of length \(2p^m\)
Recommended article: Linear complexity and autocorrelation values of a polyphase generalized cyclotomic sequence of length \(pq\)
Recommended article: Q5127800
Recommended article: Q5193632
Recommended article: The linear complexity of generalized cyclotomic binary sequences of period \(p^n\)
Recommended article: Linear complexity over \(\mathbb{F}_q\) and 2-adic complexity of a class of binary generalized cyclotomic sequences with good autocorrelation
Recommended article: Linear complexity of generalized cyclotomic sequences with period \(p^nq^m\)
Recommended article: Q5400144
Recommended article: Cryptanalysis of public key cryptosystems based on non-Abelian factorization problems
description: scientific article; zbMATH DE number 7363793