一种求循环码对偶码的新方法

本文应用离散傅里叶变换来分析有限域上时域多项式环和它的频域多项式环之间的同构,从另一角度提出了一种由循环码单位元生成它的对偶码的新方法。本文还建立了循环码单位元与它的频域单位元之间的联系,由此可以很方便地生成它的对偶码,理论和实例表明这种方法是行之有效的。     

分圆域中的线性分组码

为实现面向多维信号有限域上的编码,本文从素元出发,利用素元生成的理想为素理想,研究对任意正整数n,分圆域Q(e2πi/n)的代数整数环模素理想所得的剩余域.当错误取值于有限域乘群的一个循环子群时,这种方法得到的有限域上面向ψ(n)维信号的线性分组码可以纠单个错,从而为码调制提供了一种代数渐进方法,推广了文[3-5]中的结果.     

分圆域中的线性分组码

为实现面向多维信号有限域上的编码,本文从素元出发,利用素元生成的理想为素理想,研究对任意正整数n,分圆域Q(e2πi/n)的代数整数环模素理想所得的剩余域.当错误取值于有限域乘群的一个循环子群时,这种方法得到的有限域上面向 (n)维信号的线性分组码可以纠单个错,从而为码调制提供了一种代数渐进方法,推广了文[3-5]中的结果.     

区间判断AHP在江苏省区域经济水平综合评价中的应用

本文通过对区域和区域经济概念的研究，构建了区域经济发展水平的评价指标体系，并利用以区间特征根法为单排序方法的区间判断层次分析法对江苏省13个省辖市的经济发展水平进行了综合评价，最后对江苏省区域经济发展水平综合排序结果进行了对比分析，对江苏省区域经济发展提出了建议。     

2013年湖北竞赛解几试题的简证和它的逆命题

文[1]中，徐全德老师对2013年湖北高中竞赛解几试题进行了简证并对该问题作了推广和引申．我看了很受启发，也对这道试题进行别证，并给出其逆命题，供大家一起学习．     

嘉兴地区农村经济发展战略模型

本课题通过嘉兴地区农村经济现状分析，在建立地区农村经济评价指标体系基础上，利用灰色系统原理，对农村经济内部进行关联度分析．利用多元分析方法对３０３户抽样调查资料进行了处理．利用系统动力学原理，对嘉兴地区乡村工业建立了ＳＤ模型并进行政策性仿真．通过定性和定量分析，充分研究了地区农村经济的发展战略，为嘉兴地区农村经济的进一步发展提供了理论依据．     

基于SEIR模型的COVID-19疫情防控效果评估和预测

通过对COVID-19疫情在中国的传播情况进行分析，建立了一个SEIR流行病模型，模型中将确诊人群分成已收治和未收治两类.先从理论上分析了模型的无病平衡点及其稳定性、基本再生数等关键问题；再结合实际数据，对武汉封城前和封城后两个阶段疫情的发展趋势进行数值模拟和比较分析，讨论了模型中一些重要参数对确诊人数的影响；最后，针对上述理论分析和数值模拟的结果，对之前采取的一些控制策略作了分析评估，同时对疫情后期发展进行预测.     

市场竞争条件下的供应商选址模型研究

文章通过建立一个选址决策模型，对已有一个供应商存在的情况下，新进入该地区市场的供应商为获得最大的市场份额如何进行有效的选址决策进行了研究。在给定四个假设的基础上，构造了一个非线性规划问题，提出了进行区位决策的迭代算法，并对如何解决已有多个供应商及顾客有偏好的复杂情况进行了讨论。论文研究表明，在动态选址过程中，供应商从最大程度地占有市场的目标出发，倾向于定位在一个特定的市场吸引点。     

三角形的一个向量性质再探究

文[1]给出了三角形重心向量的一个性质，并进行了空间拓广．文[2]对三角形内任一点的向量性质进行了探究，并进行了空间拓广．文[3]对文[1]的性质进行再探究，本文类比文[3]对文[2]的性质进行再探究，得到了两个定理，现叙述如下．     

商业银行资产负债比例管理绩效综合评价的AHP模型研究

对商业银行资产负债比例管理绩效进行综合评价，是商业银行提高经营管理水平和中央银行实施货币政策目标的双重需要．本文主要讨论了运用层次分析法对其进行综合评价的程序及模型，并对该程序、模型的适用性进行了实证分析．     

Quotients of orders in algebras obtained from skew polynomials with applications to coding theory

We describe families of nonassociative finite unital rings that occur as quotients of natural nonassociative orders in generalized nonassociative cyclic division algebras over number fields. These natural orders have already been used to systematically construct fully diverse fast-decodable space-time block codes. We show how the quotients of natural orders can be employed for coset coding. Previous results by Oggier and Sethuraman involving quotients of orders in associative cyclic division algebras are obtained as special cases.     

Self-orthogonal codes constructed from orbit matrices of 2-designs and quotient matrices of divisible designs

In 2003 Harada and Tonchev showed a construction of self-orthogonal codes from orbit matrices of block designs with fixed-point-free automorphisms. We describe a construction of self-orthogonal codes from orbit matrices of 2-designs admitting certain automorphisms with fixed points (and blocks). Further, we present a construction of self-orthogonal codes from quotient matrices of divisible designs and divisible design graphs.     

两类组合设计及其在认证码中的应用

W．Ogata等定义了两种新的组合设计：外差族（EDF）与外平衡不完全区组设计（E-BIBD）．本文首先用有限域中的分圆类给出EDF的一个构造；接着用EBIBD构造出具有完善保密性的最优分裂A-码，然后证明了由满足一定条件的两个EBIBD通过上述方法构造出的两个认证码是同构的.     

多个接收者认证码的信息论下界及其组合特征

对一般的（带保密的）多个接收者认证码进行了讨论，给出了这类认证码的ｒ阶欺骗攻击成功概率的信息论下界，并利用部分平衡ｔ－设计和狭义区组设计刻划了达到信息论下界的多个接收者认证码的组合特征。     

Peterson–Gorenstein–Zierler algorithm for skew RS codes

We design a non-commutative version of the Peterson–Gorenstein–Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In particular, our decoding algorithm applies for block codes beyond the classical cyclic case.     

Self-dual codes from orbit matrices and quotient matrices of combinatorial designs

In this paper we give constructions of self-orthogonal and self-dual codes, with respect to certain scalar products, with the help of orbit matrices of block designs and quotient matrices of symmetric (group) divisible designs (SGDDs) with the dual property. First we describe constructions from block designs and their extended orbit matrices, where the orbit matrices are induced by the action of an automorphism group of the design. Further, we give some further constructions of self-dual codes from symmetric block designs and their orbit matrices. Moreover, in a similar way as for symmetric designs, we give constructions of self-dual codes from SGDDs with the dual property and their quotient matrices.     

There exist non‐isomorphic STS(19) with equivalent point codes

The rows of a point by block incidence matrix of a design can be used to generate a code, the point code of the design. It is known that binary point codes of non‐isomorphic Steiner triple systems of order hr STS(v), are inequivalent when v ≤ 15, but whether this also holds for higher orders has been open. In the current paper, an example of two non‐isomorphic STS(19) with equivalent point codes is presented. © 2004 Wiley Periodicals, Inc.     

低密度奇偶校验码的构造

低密度奇偶校验码(LDPC)最早是由Gallager于1962年提出.它们是线性分组码,其比特错误率极大地接近香农界.1995年Mackay和Neal发掘了LDPC码的新应用后,LDPC码引起了人们的广泛关注.本文利用组合结构给出一些新的LDPC码:利用可分组设计构造一类Tanner图中不含四长圈的正则LDPC码.     

Multiplicative groups used for coding QAM signals

Recently, some multiplicative groups of algebraic integers wereused to obtain quadrature amplitude modulation (QAM) signalspaces and to design error-correcting codes. This paper showsthat one subgroup of the multiplicative group of units in thealgebraic integer ring of each quadratic number field with uniquefactorization property Q(m), modulo the ideal (2ⁿ), can be usedto obtain a QAM signal space of 2^2n–2 points with goodgeometrical properties, where n 3, m 1 (mod 8) and m is asquare-free rational integer. These QAM signals can be codedsuch that a differentially coherent method can be applied todemodulate the QAM signals. The multiplicative subgroups canalso be used to construct block codes over Gaussian integerswhich are able to correct some error patterns.     

Skew codes of prescribed distance or rank

In this paper we generalize the notion of cyclic code and construct codes as ideals in finite quotients of non-commutative polynomial rings, so called skew polynomial rings of automorphism type. We propose a method to construct block codes of prescribed rank and a method to construct block codes of prescribed distance. Since there is no unique factorization in skew polynomial rings, there are much more ideals and therefore much more codes than in the commutative case. In particular we obtain a [40, 23, 10]₄ code by imposing a distance and a [42,14,21]₈ code by imposing a rank, which both improve by one the minimum distance of the previously best known linear codes of equal length and dimension over those fields. There is a strong connection with linear difference operators and with linearized polynomials (or q-polynomials) reviewed in the first section.