New sets with large Borsuk numbers

We construct finite sets in , n298, which cannot be partitioned into n+11 parts of smaller diameter thus decreasing the smallest dimension in which Borsuk's conjecture is known to be false.     

Proof of Conjectures on the True Dimension of Some Binary Goppa Codes

There is a classical lower bound on the dimension of a binary Goppa code. We survey results on some specific codes whose dimension exceeds this bound, and prove two conjectures on the true dimension of two classes of such codes.Part of this work has been presented at the Sixth International Conference on Finite Fields and Applications, Oaxaca, Mexico, May 2001.AMS classification: 94B65     

Asymptotically Good Codes from Generalized Algebraic-Geometry Codes

We consider generalized algebraic-geometry codes, based on places of the same degree of a fixed algebraic function field over a finite field. In this note, using a method similar to the Justesen’s one, we construct a family of such codes which is asymptotically good.Communicated by: D. Jangnickel     

Synchronization of quaternion-valued coupled systems with time-varying coupling via event-triggered impulsive control

In this paper, the problem of exponential synchronization of quaternion-valued coupled systems based on event-triggered impulsive control is investigated for the first time. It should be pointed out that the coupling strength is quaternion-valued and time-varying, which makes our model more in line with practical models. First, we prove that event-triggered impulsive control can exclude Zeno behavior. Then, based on the Lyapunov method and the graph theory, some sufficient conditions are derived to ensure that quaternion-valued coupled systems reach synchronization. Furthermore, as an application of our theoretical results, exponential synchronization of quaternion-valued Kuramoto oscillators is studied in detail and a synchronization criterion is presented. Finally, some numerical simulations are given to show the effectiveness of our theoretical results.     

Bounds for binary multiple covering codes

We study codes that are multiple coverings of the Hamming space and discuss lower and upper bounds onK(n, r, ), the minimum cardinality of a binary code of lengthn such that the Hamming spheres of radiusr centered at the codewords cover at least times. We also study the similar problem of multiple coverings containing repeated words. A table of bounds forn16,r4, 4 is given.     

Asymptotic stability of switched linear time-varying systems based on top-floor function

This paper considers the problem of asymptotic stability for switched linear time-varying (SLTV) systems. First, some stability conditions for SLTV systems are given by using infinite integrals. Then, based on the results obtained, two stability conditions are proposed by combining the methods of top-floor function and average dwell time. Moreover, using strict top-floor function, a stability condition is also provided when some subsystems are unstable. With the help of top-floor function, the stability problem of SLTV systems can be simplified and solved by using the technique of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the theoretical results.     

两类子域码的重量分布（英文）

子域码是一类特殊的线性码.线性码由于其有效的编码及译码算法,在电子消费产品、数据存储系统和通信系统中有广泛的应用.然而,确定线性码的重量分布通常是困难的工作.本文给出了两类二元子域码C₍₍H(f)_<sub>1))~((2))和C₍₍H(f)_<sub>2))~((2))及其对偶码的重量分布,其中f₁(x)=x~4,f₂(x)=x~6+x~4+x~2.     

Counting polynomials over finite fields with prescribed leading coefficients and linear factors

We count the number of polynomials over finite fields with prescribed leading coefficients and a given number of linear factors. This is equivalent to counting codewords in Reed-Solomon codes which are at a certain distance from a received word. We first apply the generating function approach, which is recently developed by the author and collaborators, to derive expressions for the number of monic polynomials with prescribed leading coefficients and linear factors. We then apply Li and Wan's sieve formula to simplify the expressions in some special cases. Our results extend and improve some recent results by Li and Wan, and Zhou, Wang and Wang.     

A formula on the weight distribution of linear codes with applications to AMDS codes

The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and codes with small Singleton's defect. We propose a new set of linear relations that must be satisfied by the coefficients of the weight distribution. From these relations we are able to derive known identities (in an easier way) for interesting cases, such as extremal codes, Hermitian codes, MDS and NMDS codes. Moreover, we are able to present for the first time the weight distribution of AMDS codes. We also discuss the link between our results and the Pless equations.