具变时滞的变系数线性差分系统零解的指数稳定性

本文通过建立一个线性差分不等式,利用向量V函数法,研究了一类具变时滞的变系数线性差分系统零解的指数稳定性,给出了一些简单的稳定性代数判据。     

代数函数域上的局部恢复码

假设C是有限域Fq上的[n,k]线性码,如果码字的每个坐标是其它至多r个坐标的函数,称C是(n,k,r)线性码,这里r是较小的数.本文在代数函数域上构造出了局部恢复码,它的码长不受字符集大小的限制,实际上,它的码长可以远远大于字符集的大小;并将此方法应用于广义Hermite函数域,得到了一类广义Hermite函数域上的局部恢复码.进一步地,通过构造子码的方式改进了广义Hermite函数域上的局部恢复码的最小距离的下界.     

非线性扰动广义NNV微分系统的孤子研究

采用了一个简单而有效的技巧,研究了一类非线性扰动广义NNV微分系统.首先引入一个行波变换,将NNV系统转化为一组非线性常微分方程系统.其次用双曲函数待定系数法得到一个相应的典型系统的孤子解·然后构造一个广义泛函迭代同伦映射,由此构造一个特殊的渐近解的迭代关系式.并依次地求出原非线性扰动广义NNV微分系统的孤子渐近行波解.最后通过举例,说明了使用本方法得到的近似解简单而有效.     

广义半交换环的幂零结构

研究了广义半交换环的幂零结构,定义了一类新的环类,即幂零$\alpha$-半交换环.说明了$\alpha$-半交换环与半交换环, $\alpha$-半交换环和$\alpha$-刚性环等环密切相关,通过构造反例说明了幂零$\alpha$-半交换环未必是$\alpha$-半交换环.研究了幂零$\alpha$-半交换环的各种性质,推广和统一了与环的半交换性质有关的若干结论.     

二阶非线性阻尼泛函差分方程的振动性定理

研究一类具阻尼项的二阶广义Emden-Fowler型变时滞的泛函差分方程的振动性,通过引入二重序列H_(n,s),并结合一些经典不等式,获得了该类差分方程振动的4个新的充分条件,所得结果反应了时滞项和阻尼项在差分系统振动中的影响作用.     

有限域上的广义准多项式码

文章提出了一类新的码——广义准多项式码,它是多项式码的一种推广.文中首先给出了广义准多项式码的概念及其生成矩阵的结构,然后重点研究了1-生成元的广义准多项式码参数的相关性质,并且基于这些性质构造出了一些最优码.     

完美非线性映射的一类构造

在分组密码中 ,为了抗差分攻击 ,需要完美非线性映射 .利用有限域 Zp上的广义 Bent函数和不可约多项式 ,给出了完美非线性映射的一类构造 .     

完备的$\nu$-广义度量空间上的不动点定理[英文]

本文对度量空间中$C$类函数的压缩映射进行推广. 在完备的$\nu$-广义度量空间上, 利用构造迭代序列的方法, 证明了关于($\psi$,$\phi$)-类型压缩映射的不动点定理. 并且证明了广义的$F$类型压缩和广义$\theta$类型压缩映射.     

一类四阶非线性系统的李雅普诺夫函数构造和零解稳定性

计算出了四阶常系数线性系统的各种形式的李雅普诺夫函数,并将四阶非线性系统化成它的等价系统,通过类比的方法构造出一类四阶非线性系统的李雅普诺夫函数,从而获得该系统零解全局渐近稳定的充分条件.     

广义基插值的正交多尺度函数和多小波

给出一类具有广义插值的正交多尺度函数的构造方法, 并给出对应多小波的显示构造公式. 证明了该文构造的多小波拥有与多尺度函数相同的广义基插值性.从而建立了多小波子空间上的采样定理. 最后基于该文提供的算法构造出若干具有广义基插值的正交多尺度函数和多小波.     

Optimal and perfect difference systems of sets

Difference systems of sets (DSS) were introduced in 1971 by Levenstein for the construction of codes for synchronization, and are closely related to cyclic difference families. In this paper, algebraic constructions of difference systems of sets using functions with optimum nonlinearity are presented. All the difference systems of sets constructed in this paper are perfect and optimal. One conjecture on difference systems of sets is also presented.     

A class of optimal constant composition codes from GDRPs

As a common generalization of constant weight binary codes and permutation codes, constant composition codes (CCCs) have attracted recent interest due to their numerous applications. In this paper, a class of new CCCs are constructed using design-theoretic techniques. The obtained codes are optimal in the sense of their sizes. This result is established, for the most part, by means of a result on generalized doubly resolvable packings which is of combinatorial interest in its own right.      

Optimal and perfect difference systems of sets from <Emphasis Type="Italic">q</Emphasis>-ary sequences with difference-balanced property

Difference systems of sets (DSS) are important for the construction of codes for synchronization. In this paper, a general construction of optimal and perfect difference systems of sets based on q-ary sequences of period n = −1 (mod q) with difference- balanced property is presented, where q is a prime power. This works for all the known q-ary sequences with ideal autocorrelation, and generalizes the earlier construction based on ternary sequences with ideal autocorrelation. In addition, we construct another class of optimal and perfect difference systems of sets, employing decimation of q-ary d-form sequences of period q ^m −1 with difference-balanced property, which generalizes the previous construction from power functions.     

A link between combinatorial designs and three-weight linear codes

In this paper, we show that partial geometric designs can be constructed from certain three-weight linear codes, almost bent functions and ternary weakly regular bent functions. In particular, we show that existence of a family of partial geometric difference sets is equivalent to existence of a certain family of three-weight linear codes. We also provide a link between ternary weakly regular bent functions, three-weight linear codes and partial geometric difference sets.     

Constructions of optimal difference systems of sets

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.     

Generic constructions for partitioned difference families with applications: a unified combinatorial approach

Partitioned difference families are an interesting class of discrete structures which can be used to derive optimal constant composition codes. There have been intensive researches on the construction of partitioned difference families. In this paper, we consider the combinatorial approach. We introduce a new combinatorial configuration named partitioned relative difference family, which proves to be very powerful in the construction of partitioned difference families. In particular, we present two general recursive constructions, which not only include some existing constructions as special cases, but also generate many new series of partitioned difference families. As an application, we use these partitioned difference families to construct several new classes of optimal constant composition codes.     

Linear codes with few weights from weakly regular plateaued functions

Linear codes with few nonzero weights have wide applications in secret sharing, authentication codes, association schemes and strongly regular graphs. Recently, Wu et al. (2020) obtained some few-weighted linear codes by employing bent functions. In this paper, inspired by Wu et al. and some pioneers' ideas, we use a kind of functions, namely, general weakly regular plateaued functions, to define the defining sets of linear codes. Then, by utilizing some cyclotomic techniques, we construct some linear codes with few weights and obtain their weight distributions. Notably, some of the obtained codes are almost optimal with respect to the Griesmer bound. Finally, we observe that our newly constructed codes are minimal for almost all cases.     

Binary linear codes with few weights from Boolean functions

Boolean functions have very nice applications in coding theory and cryptography. In coding theory, Boolean functions have been used to construct linear codes in different ways. The objective of this paper is to construct binary linear codes with few weights using the defining-set approach. The defining sets of the codes presented in this paper are defined by some special Boolean functions and some additional restrictions. First, two families of binary linear codes with at most three or four weights from Boolean functions with at most three Walsh transform values are constructed and the parameters of their duals are also determined. Then several classes of binary linear codes with explicit weight enumerators are produced. Some of the binary linear codes are optimal or almost optimal according to the tables of best codes known maintained at http://www.codetables.de, and the duals of some of them are distance-optimal with respect to the sphere packing bound.

     

Constructing few-weight linear codes and strongly regular graphs

Linear codes with few weights have applications in data storage systems, secret sharing schemes, graph theory and so on. In this paper, we construct a class of few-weight linear codes by choosing defining sets from cyclotomic classes and we also establish few-weight linear codes by employing weakly regular bent functions. Notably, we get some codes that are minimal and we also obtain a class of two-weight optimal punctured codes with respect to the Griesmer bound. Finally, we get a class of strongly regular graphs with new parameters by using the obtained two-weight linear codes.     

A generalization of combinatorial designs and related codes

In this paper we study a certain generalization of combinatorial designs related to almost difference sets, namely the t-adesign, which was coined by Ding (Codes from difference sets, 2015). It is clear that 2-adesigns are partially balanced incomplete block designs which naturally arise in many combinatorial and statistical problems. We discuss some of their basic properties and give several constructions of 2-adesigns (some of which correspond to new almost difference sets and some to new almost difference families), as well as two constructions of 3-adesigns. We discuss basic properties of the incidence matrices and make an initial investigation into the codes which they generate. We find that many of the codes have good parameters in the sense they are optimal or have relatively high minimum distance.