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New Results on Nonexistence of Perfect p-Ary Sequences and Almost p-Ary Sequences

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Acta Mathematica Sinica,English Series 2016年第1期32卷 2-10页

作者： Hai Ying LIU Ke Qin FENG School of Mathematical Sciences Peking University Department of Mathematical Sciences Tsinghua University

Complex periodical sequences with lower antocorrelation values are used in CDMA comnmnieation systems and cryptography. In this paper we present new nonexistence results on perfect p-ary sequences and almost p-ary seq... 详细信息

关键词： Perfect sequence p-ary and almost p-ary sequence difference set cyclotomic field imag-inary quadratic field

Diference Systems of sets Based on Cosets Partitions

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Acta Mathematica Sinica,English Series 2013年第12期29卷 2261-2272页

作者： Geng Sheng ZHANG Hong Rui WANG College of Mathematics and Information Science Hebei Normal University Hebei Key Laboratory of Computational Mathematics and Applications

difference systems of sets （DSS） are combinatorial configurations that arise in connection with code synchronization. This paper proposes a new method to construct DSSs, which uses known DSSs to partition some of the cosets of Zv relative to subgroup of order k, where v = km is a composite number. As applications, we obtain some new optimal DSSs.

关键词： difference systems of sets code synchronization difference set coset optimal

Constructions of optimal difference systems of sets

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Science China Mathematics 2011年第1期54卷 173-184页

作者： FAN CuiLing LEI JianGuo SHAN XiuLing School of Sciences Nantong University Nantong 226007 China College of Mathematics and Information Science Hebei Normal University Shijiazhuang 050016 China

difference systems of sets (DSSs) are combinatorial configurations which were introduced in 1971 by Levenstein for the construction of codes for synchronization. In this paper, we present two kinds of constructions of difference systems of sets by using disjoint difference families and a special type of difference sets, respectively. As a consequence, new infinite classes of optimal DSSs are obtained.

关键词： difference system of sets code synchronization optimal disjoint difference family difference set

The ranks of Maiorana-McFarland bent functions

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Science China Mathematics 2008年第9期51卷 1726-1731页

作者： WENG GuoBiao FENG RongQuan QIU WeiSheng ZHENG ZhiMing LMAM School of Mathematical SciencesPeking UniversityBeijing 100871China

In this paper, the ranks of a special family of Maiorana-McFarland bent functions are discussed. The upper and lower bounds of the ranks are given and those bent functions whose ranks achieve these bounds are determined. As a consequence, the inequivalence of some bent functions are derived. Furthermore, the ranks of the functions of this family are calculated when t 6.

关键词： p-rank bent function difference set 06E30 11T71 94C10

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4p^2q^2b阶群中的Menon差集

Northeastern Mathematical Journal 1997年第4期13卷 482-486页

作者：万兆泽 Peking University 100871 Beijing Department of Mathematics

In this paper we study the existence of abelian Menon difference sets with parameter (4p2q2b,wp2q2b-pqb,p2q2b-pqb)in G=H×Cp×Cp or H×Cp2 and get a necessary condition for it.

关键词： difference set Cyclic Base Intersection Number

A SURVEY OF ORTHOGONAL ARRAYS OF STRENGTH TWO

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Acta Mathematicae Applicatae Sinica 1995年第3期11卷 308-317页

作者：刘璋温井淑夫 Institute of Applied Mathematics the Chinese Academy of Sciences Beijing China Okayama University of Science Japan International Institute for Natural Sciences Kurashiki Japan

The purpose of this paper is to survey the construction of orthogonal arrays of strength two by using difference sets. Some methods for constructing difference set D(2p.2p,p,2), where p is a prime or a prime power, are given. It is shown that the Kronecker sum of a difference set D(λ1p, k1, p, 2) and an orthogonal array(λ2p2, k2, p, 2) leads to another orthogonal array (λ1λ2p3 .k1k2+1 ,p, 2). This enables us to construct orthogonal arrays[2p(n+1)、1+2(p+p2 +…+pn),p,2],[4p(n+2),1+2p+4(p2+p3+…+p(n+1)),p, 2],and [8p(n+3),1+2P+4p2+8(p3+p4+…+p(n+2)),p,2]where p is a prime or a prime power.

关键词： Orthogonal array difference set kronecker sum affine resolvable BIB design

Feature Selection Based on difference and Similitude in Data Mining

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Wuhan University Journal of Natural Sciences 2007年第3期12卷 467-470页

作者： WU Ming YAN Puliu School of Electronic Information Wuhan University Wuhan 430072 Hubei China

Feature selection is the pretreatment of data mining. Heuristic search algorithms are often used for this subject. Many heuristic search algorithms are based on discernibility matrices, which only consider the difference in information system. Because the similar characteristics are not revealed in discernibility matrix, the result may not be the simplest rules. Although differencesimilitude（DS） methods take both of the difference and the similitude into account, the existing search strategy will cause some important features to be ignored. An improved DS based algorithm is proposed to solve this problem in this paper. An attribute rank function, which considers both of the difference and similitude in feature selection, is defined in the improved algorithm. Experiments show that it is an effective algorithm, especially for large-scale databases. The time complexity of the algorithm is O（｜ C ｜^2｜U ｜^2）.

关键词： knowledge reduction feature selection rough set difference set similitude set attribute rank function

A Kind of Diophantine Equations in Finite Simple Groups

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Northeastern Mathematical Journal 2000年第4期16卷 391-397页

作者：曹珍富 Harbin Institute of Technology

In this paper, we prove that if p, q are distinct primes, (p,q)≡(1,7) (mod 12) and Legendres symbol pq=1 , then the equation 1+p a=2 bq c+2 dp eq f has only solutions of the form (a,b,c,d,e,f)=(t,0,0,0,t,0), where t is a non negative integer. We also give all solutions of a kind of generalized Ramanujan Nagell equations by using the theories of imaginary quadratic field and Pells equation.

关键词： exponential Diophantine equation generalized Ramanujan Nagell equation finite simple group difference set