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Fast algorithm for determining the minimal polynomial of up^n-periodic sequence

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Journal of Southeast University(English Edition) 2012年第3期28卷 367-371页

作者：胡卫群岳勤南京林业大学理学院南京210037 南京航空航天大学理学院南京210016

A fast algorithm for determining the minimal polynomial and linear complexity of a upn-periodic sequence over a finite field Fq is *** p,q,and u be distinct primes,q a primitive root modulo p2,m the smallest positive integer such that qm≡1 mod u,and gcd（m,p（p-1））=*** algorithm is used to reduce a periodic upn sequence over Fq to several pn-periodic sequences over Fq（ζ）,where ζ is a u-th primitive root of unity,and an algorithm proposed by Xiao et *** employed to obtain the minimal polynomial of each pn-periodic sequence.

关键词： minimal polynomial linear complexity periodic sequence

R-matrix for the 8-Dimensional Spin Representation of Uq(so7)

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Acta Mathematica Sinica,English Series 2024年第2期40卷 485-497页

作者： Hong Mei HU Nai Hong HU School of Mathematical Sciences Suzhou University of Science and TechnologySuzhou 215009P.R.China School of Mathematical Sciences MOE Key Laboratory of Mathematics and Engineering Applications&Shanghai Key Laboratory of PMMPEast China Normal UniversityShanghai 200241P.R.China

The purpose of the paper is to describe the solution to the quantum Yang-Baxter equation associated with the 8-dimensional spin representation Tsp of Uq(so7).The self-duality of Tsp and the symmetry of the corresponding braiding matrix are ***,the minimal polynomial of the braiding R-matrix of Tsp is presented explicitly in an ingenious method by taking advantage of nice features of the spin representation Tsp.

关键词： Braiding R-matrix spin module minimal polynomial

Exact Bivariate polynomial Factorization over Q by Approximation of Roots

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Journal of Systems Science & Complexity 2015年第1期28卷 243-260页

作者： FENG Yong WU Wenyuan ZHANG Jingzhong CHEN Jingwei Chongqing Key Lab of Automated Reasoning and Cognition Chongqing Institute of Green and Intelligent Technology(CIGIT)Chinese Academy of Sciences

Factorization of polynomials is one of the foundations of symbolic *** applications arise in numerous branches of mathematics and other ***,the present advanced programming languages such as C++ and J++,do not support symbolic computation ***,it leads to difficulties in applying factorization in engineering *** this paper,the authors present an algorithm which use numerical method to obtain exact factors of a bivariate polynomial with rational *** proposed method can be directly implemented in efficient programming language such C++ together with the GNU Multiple-Precision *** addition,the numerical computation part often only requires double precision and is easily parallelizable.

关键词： Factorization of multivariate polynomials interpolation methods minimal polynomial numerical continuation.

A note for preconditioning nonsymmetric matrices

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 93-100页

作者： CHEN Xiao-shan LI Wen School of Mathematics, South China Normal University, Guangzhou 510631, China School of Mathematics South China Normal University Guangzhou China

In this paper, we consider preconditioners for generalized saddle point systems with a nonsymmetric coefficient matrix. A constraint preconditioner for this systems is constructed, and some spectral properties of the ... 详细信息

关键词： Preconditioner saddle point matrix minimal polynomial Schilder's factorization.

Linear Complexity of New Generalized Cyclotomic Sequences of Length 2pq

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Transactions of Nanjing University of Aeronautics and Astronautics 2014年第6期31卷 710-716页

作者：王宏伟葛武 Civil Construction Engineering Department Hubei Polytechnic University Zhejiang Education Publishing House

The linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are investigated.A new generalized cyclotomic sequence Sof length 2pqis defined with an imbalance p+*** results show th... 详细信息

关键词： generalized cyclotomic sequence linear complexity minimal polynomial

A property of Pisot numbers and Fourier transforms of self-similar measures

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Science China Mathematics 2012年第8期55卷 1721-1733页

作者： HU Tian-You Department of Mathematics University of Wisconsin-Green Bay Wisconsin WI 54311 USA

For any Pisot number β it is known that the set F（β） ={t ： limn→∞‖tβn‖ = 0} is countable, where ‖α‖ is the distance between a real number a and the set of integers. In this paper it is proved that every member in this set is of the form cβn, where n is a nonnegative integer and e is determined by a linear system of equations. Furthermore, for some self-similar measures μ associated with β, the limit at infinity of the Fourier transforms limn→μ（tβn）≠0 if and only if t is in a certain subset of F（β）. This generalizes a similar result of Huang and Strichartz.

关键词： Bernoulli convolution Fourier transform minimal polynomial Pisot number recurrence relation,self-similar measure

A fast algorithm for determining the linear complexity of a binary sequence with period 2~np^m

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Science in China(Series F) 2001年第6期44卷 453-460页

作者：魏仕民肖国镇陈钟 Information Security Research Group Department of Computer Science and Technique Peking UniversityBeijing 100871 China Department of Mathematics Huaibei Coal Normal College Huaibei 235000 China National Key Laboratory of ISN Xidian University Xi'

An efficient algorithm for determining the linear complexity and the minimal polynomial of a binary sequence with period 2npm is proposed and proved, where 2 is a primitive root modulo p2. The new algorithm generalizes the algorithm for computing the linear complexity of a binary sequence with period 2' and the algorithm for computing the linear complexity of a binary sequence with period pn, where 2 is a primitive root modulo p2.

关键词： cryptography periodic sequence linear complexity minimal polynomial fast algorithm.

Two Eigenvector Theorems

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Advances in Linear Algebra & Matrix Theory 2016年第1期6卷 11-16页

作者： Raghuram Prasad Dasaradhi V. V. Haragopal Department of Mathematics Osmania University Hyderabad India Department of Statistics Osmania University Hyderabad India

In this paper, we established a connection between a square matrix “A” of order “n” and a matrix defined through a new approach of the recursion relation . (where is any column matrix with n real elements). Now the new matrix gives us a characteristic equation of matrix A and we can find the exact determination of Eigenvalues and its Eigenvectors of the matrix A. This new approach was invented by using Two eigenvector theorems along with some examples. In the subsequent paper we apply this approach by considering some examples on this invention.

关键词： Characteristic Equation minimal polynomial Eigenvalues Eigenvectors Vander Monde Matrix Jacobi Block Matrix

Linear complexity of Ding generalized cyclotomic sequences

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Journal of Shanghai University(English Edition) 2007年第1期11卷 22-26页

作者：闫统江陈智雄肖国镇 ISN National Key Laboratory Xidian University

minimal polynomials and linear complexity of binary Ding generalized cyclotomic sequences of order 2 with the two-prime residue ring Zpq are obtained by Bai in 2005. In this paper, we obtain linear complexity and minimal polynomials of all Ding generalized cyclotomic sequences. Our result shows that linear complexity of these sequences takes on the values pq and pq-1 on our necessary and sufficient condition with probability 1/4 and the lower bound （pq - 1）/2 with probability 1/8. This shows that most of these sequences are good. We also obtained that linear complexity and minimal polynomials of these sequences are independent of their orders. This makes it no more difficult in choosing proper p and q.

关键词： stream cipher generalized cyclotomic sequence linear complexity minimal polynomial