CYCLOTOMY

作品数：13被引量：27H指数：3
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Generalized Cyclotomic Mappings: Switching Between Polynomial, Cyclotomic, and Wreath Product Form
《Communications in Mathematical Research》2022年第2期246-318,共73页Alexander Bors Qiang Wang 
This paper is concerned with so-called index d generalized cyclotomic mappings of a finite field F_(q), which are functions F_(q)→F_(q) that agree with a suitable monomial function x↦axr on each coset of the index d ...
关键词：Finite fields CYCLOTOMY cyclotomic mappings permutation polynomials wreath product cycle structure INVOLUTION 
A Small Correction to a Paper of Vandermonde
《Open Journal of Discrete Mathematics》2021年第2期43-53,共11页Matthew Davis Shiv K. Gupta 
In this paper using elementary Galois Theory, we give a detailed explanation of the calculation of the radical expression for
《Chinese Journal of Electronics》2021年第2期232-237,共6页LIU Junying JIANG Yupeng ZHENG Qunxiong LIN Dongdai 
supported by the National Natural Science Foundation of China(No.11701553,No.61872358,No.61872359);the National Postdoctoral Program for Innovative Talents(No.BX201600188);the National Science Foundation for Post-doctoral Scientists of China(No.2017M611035);Young Elite Scientists Sponsorship Program by CAST(No.2016QNRC001)。
As a kind of generators of pseudorandom sequences,the Feedback shift register(FSR)is widely used in channel coding,cryptography and digital communication.A necessary and sufficient condition for the nonsingularity of ...
关键词：Feedback shift register(FSR) NONSINGULARITY Permutation polynomial CYCLOTOMY Quadratic form 
On Cyclic Codes with Length 2p^e over Finite Fields
《Chinese Journal of Electronics》2020年第4期672-677,共6页PANG Binbin ZHU Shixin SUN Zhonghua 
supported by the National Natural Science Foundation of China(No.61772168,No.61572168);the Natural Science Foundation of Anhui Province(No.1708085QA01,No.2008085QA04)。
Cyclic codes are an important class of linear codes.Cyclic codes are applied in data storage,communication systems and consumer electronics due to their efficient encoding and decoding algorithms.We utilize the cyclot...
关键词：Cyclic codes CYCLOTOMY HULL Primitive root 
New quaternary sequences of even length with optimal auto-correlation被引量：7
《Science China(Information Sciences)》2018年第2期121-133,共13页Wei SU Yang YANG Zhengchun ZHOU Xiaohu TANG 
Wei SU was supported by National Science Foundation of China(Grant No.61402377);in part supported by Open Research Subject of Key Laboratory(Research Base)of Digital Space Security(Grant No.szjj2014-075);Science and Technology on Communication Security Laboratory(Grant No.9140C110302150C11004);Yang YANG was supported by National Science Foundation of China(Grants Nos.61401376,11571285);Application Fundamental Research Plan Project of Sichuan Province(Grant No.2016JY0160);Zhengchun ZHOU and Xiaohu TANG was supported by National Science Foundation of China(Grants Nos.61672028,61325005)
Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length N can...
关键词：binary sequences quaternary sequences Gray mapping interleaving cyclotomy 
On the Linear Complexity of New Generalized Cyclotomic Binary Sequences of Order Two and Period pqr被引量：4
《Tsinghua Science and Technology》2016年第3期295-301,共7页Longfei Liu Xiaoyuan Yang Xiaoni Du Bin Wei 
supported by the National Natural Science Foundation of China (Nos.61272492,61103231,61202492,61202395,61462077,and 61562077);the Program for New Century Excellent Talents in University (No.NCET-12-0620)
Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental ...
关键词：stream cipher pseudorandom sequence generalized cyclotomy linear complexity 
GAUSS PERIODS AND CYCLIC CODES FROM CYCLOTOMIC SEQUENCES OF SMALL ORDERS被引量：1
《Journal of Electronics(China)》2014年第6期537-546,共10页Hu Liqin Yue Qin Zhu Xiaomeng 
Supported by the National Natural Science Foundation(NNSF)of China(No.11171150);Foundation of Science and Technology on Information Assurance Laboratory(No.KJ-13-001);Funding of Jiangsu Innovation Program for Graduate Education(CXLX13-127,Fundamental Research Funds for the Central Universities);Funding for Outstanding Doctoral Dissertation in NUAA(BCXJ-13-17)
Let p =ef +1 be an odd prime with positive integers e and f. In this paper, we calculate the values of Gauss periods of order e =3, 4, 6 over a finite field GF(q), where q is a prime with q≠p. As applications, severa...
关键词：Sequence Cyclic code Weight distribution Gauss period CYCLOTOMY 
Linear complexity of quaternary sequences with odd period and low autocorrelation被引量：3
《The Journal of China Universities of Posts and Telecommunications》2014年第5期89-93,共5页KE Pin-hui LIN Chang-lu ZHANG Sheng-yuan 
supported by the National Natural Science Foundation of China (61102093);the Joint Funds of the National Natural Science Foundation of China (U1304604);the Fujian Normal University Innovative Research Team (IRTL 1207)
Equivalence between two classes of quaternary sequences with odd period and best known autocorrelation are proved. A lower bound on the linear complexity of these sequences is presented. It is shown that the quaternar...
关键词：quaternary sequences linear complexity CYCLOTOMY 
Autocorrelation Value of Whiteman Generalized Cyclotomic Sequence被引量：6
《Journal of Mathematical Research with Applications》2012年第4期415-422,共8页Liqin HU Qin YUE 
Supported by the National Natural Science Foundation of China (Grant Nos. 10771100;10971250;11171150)
Let p,q be distinct primes with gcd（p-1,q-1） = 4.In this paper,we calculate the autocorrelation values of binary sequences of generalized cyclotomic sets of order four in Z pq and get conditions of p and q such that...
关键词：generalized cyclotomy generalized cyclotomic sequence autocorrelation value. 
THE CONSTRUCTIONS OF ALMOST BINARY SEQUENCE PAIRS WITH THREE-LEVEL CORRELATION BASED ON CYCLOTOMY被引量：1
《Journal of Electronics(China)》2012年第1期9-16,共8页Peng Xiuping Xu Chengqian 
Supported by the National Natural Science Foundation of China (No. 60872061,60971126,and 61172094)
In this paper,a new class of almost binary sequence pair with a single zero element is presented.The almost binary sequence pairs with three-level correlation are constructed based on cyclotomic numbers of order 2,4,a...
关键词：CORRELATION Cyclotomic numbers Almost binary sequence pairs Binary sequence pair 
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