Maximum Distance Separable Convolutional Codes

A maximum distance separable (MDS) block code is a linear code whose distance is maximal among all linear block codes of rate k/n. It is well known that MDS block codes do exist if the field size is more than n. In this paper we generalize this concept to the class of convolutional codes of a fixed rate k/n and a fixed code degree δ. In order to achieve this result we will introduce a natural upper bound for the free distance generalizing the Singleton bound. The main result of the paper shows that this upper bound can be achieved in all cases if one allows sufficiently many field elements. Received: December 10, 1998; revised version: May 14, 1999     

Bounds on Minimum Distance for Linear Codes over GF(5)

Let [n, k, d; q]-codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). Let d ₅(n, k) be the maximum possible minimum Hamming distance of a linear [n, k, d; 5]-code for given values of n and k. In this paper, forty four new linear codes over GF(5) are constructed and a table of d ₅(n, k) k≤ 8, n≤ 100 is presented.     

Optimal Formally Self-Dual Codes over ?5 and ?7

In this paper, we study optimal formally self-dual codes over ?₅ and ?₇. We determine the highest possible minimum weight for such codes up to length 24. We also construct formally self-dual codes with highest minimum weight, some of which have the highest minimum weight among all known linear codes of corresponding length and dimension. In particular, the first known [14, 7, 7] code over ?₇ is presented. We show that there exist formally self-dual codes which have higher minimum weights than any comparable self-dual codes. Received: May 18, 1998; revised version: September 4, 1999     

On the Covering Radius of Long 5-ary BCH Codes with Minimum Distance 7

 We study S. D. Cohen’s method of estimating the covering radius of long primitive non-binary BCH codes with prime field alphabet. As an application we show that the covering radius is at most 7 for long 5-ary BCH codes with minimum distance seven. Received: November 13, 1996; revised version: March 11, 1997     

内隔断布置情况对地板送风房间空气品质影响的数值模拟分析

利用CFD对室内存在不同形式内隔断的地板送风办公房间进行了数值模拟,研究其速度场、温度场及污染物浓度场;分析了内隔断的存在对室内空气品质的影响。研究结果表明,在办公桌靠近送风口侧设置的隔断,能够在一定程度上阻挡由送风口处送出的冷风直接抵达人体脚踝处,有助于改善人体脚寒的情况。但围合型隔断的存在将导致隔间内形成涡流,使人体周围的气流速度增大,并影响CO2的扩散,不利于其顺利排出。     

Note on Niederreiter-Xing's Propagation Rule for Linear Codes

We present a simple construction of long linear codes from shorter ones. Our approach is related to the product code construction; it generalizes and simplifies substantially the recent “Propagation Rule” by Niederreiter and Xing. Many optimal codes can be produced by our method. Received: June 23, 2000     

均匀B样条曲线曲面的小波表示

小波基为曲线曲面带来了更为灵活的表达方式,均匀B样条曲线曲面在经过小波分解以后所得到的小波在定义域边界与内部可以采用统一的表达式,在进行小波重构时仅需作乘法运算,计算效率高。本文试图从几何概念出发由浅入深地论述基于小波的均匀三次B样条曲线曲面多分辨表示的原理及其实现。     

Improved Bounds for Quaternary Linear Codes of Dimension 6

In this paper, twenty new codes of dimension 6 are presented which give improved bounds on the maximum possible minimum distance of quaternary linear codes. These codes belong to the class of quasi-twisted (QT) codes, and have been constructed using a stochastic optimization algorithm, tabu search. A table of upper and lower bounds for d ⁴(n,6) is presented for n≤ 200. Received: 20 December 1996 / Accepted: 13 May 1997     

Construction of Improved Geometric Goppa Codes from Klein Curves and Klein-like Curves

Linear error-correcting codes, especially Reed-Solomon codes, find applications in communication and computer memory systems, to enhance their reliability and data integrity. In this paper, we present Improved Geometric Goppa (IGG) codes, a new class of error-correcting codes, based on the principles of algebraic-geometry. We also give a reasonably low complexity procedure for the construction of these IGG codes from Klein curves and Klein-like curves, in plane and high-dimensional spaces. These codes have good code parameters like minimum distance rate and information rate, and have the potential to replace the conventional Reed-Solomon codes in most practical applications. Based on the approach discussed in this paper, it might be possible to construct a class of codes whose performance exceeds the Gilbert-Varshamov bound. Received: November 14, 1995; revised version: November 22, 1999     

遥控器用红外LED辐射强度和遥控距离的测量

本文研究了遥控器用红外ＬＥＤ辐射强度和遥控距离的测量，研制了光电探测器，建立了测试仪，分析了仪器的定标．仪器测试辐射强度的精度为７．９４％。测量的遥控距离与实际用遥控器启动接收器的结果是一致的．     

单分散球形硫化镉粒子的制备及其形貌控制

水溶液中,以聚乙烯基吡咯烷酮为表面活性剂,由沉淀法制备出硫化镉的单分散的微球颗粒材料.应用TEM和XRD等测试手段研究了随高聚物浓度的变化对硫化镉颗粒形貌的控制.结果表明,控制高聚物的浓度可以制备得到直径在500nm的单分散硫化镉微球;高聚物浓度在一定范围内,微球的直径随浓度增大而增大,且分散性越好;微球是由硫化镉的微小单晶沉积而成的,随着高聚物的浓度增大,单晶的尺寸越小.     

结合颜色不变量和ORB特征的图像匹配算法

目的针对现有图像匹配算法因忽略图像颜色信息,使算法对光照变化的鲁棒性较差,容易造成图像误匹配的情况进行改善。方法颜色信息是区分不同图像的重要特征,通过提取彩色图像颜色不变量的方法获得图像的颜色信息,并将颜色不变量与ORB特征描述子相结合,形成一种C-ORB算法,C-ORB算法在保留ORB算法优点的基础上,能够将图像的色彩信息应用到图像匹配过程当中。结果实验结果表明,结合了颜色不变量的ORB算法在保留了ORB算法运算速度快的基础上,能够在不同光照强度、不同光照方向下,获得更多的图像细节,匹配更为准确。结论在移动手机、平板电脑等移动终端设备进行印刷品识别与匹配时,能够在保证识别图像识别速度的基础上进一步减少图像的误匹配。     

Divisibility properties and new bounds for cyclic codes and exponential sums in one and several variables

Serre has obtained sharp estimates for the number of rational points on an algebraic curve over a finite field. In this paper we supplement his technique with divisibility properties for exponential sums to derive new bounds for exponential sums in one and several variables. The new bounds give us an improvement on previous bounds for the minimum distance of the duals of BCH codes. The divisibility properties also imply the existence of gaps in the weight distribution of certain cyclic codes, and in particular gives us that BCH codes are divisible (in the sense of H. N. Ward).The results of this paper were presented in the IEEE International Symposium on Information Theory, Budapest, Hungary, July 1991.This work was partially supported by the Guastallo Fellowship and the Israeli Ministry of Science and Technology under Grant 5110431.This work was partially supported by the National Science Foundation (NSF) under Grants DMS-8711566 and DMS-8712742.This work was partially supported by NSF Grants RII-9014056, the Component IV of the EPSCoR of Puerto Rico Grant, and U.S. Army Research Office through the Army Center of Excellence for Symbolic Methods in Algorithmic Mathematics (ACSyAM), of Cornell MSI. Contract DAAL03-91-C-0027.     

Duadic Codes over F2 + uF2

Duadic codes over F ₂ + u F ₂ are introduced as abelian codes by their zeros. This is the function field analogue of duadic codes over Z ₄ introduced recently by Langevin and Solé. They produce binary self-dual codes via a suitable Gray map. Their binary images are themselves abelian, thus generalizing a result of van Lint for cyclic binary codes of even length. We classify them in modest lengths and exhibit interesting non-cyclic examples. Received: April 26, 2000; revised version: May 5, 2001     

Uniform asymptotic approximations for accurate modeling of cracks in layered elastic media*

We present uniform asymptotic solutions (UAS) for displacement discontinuities (DD) that lie within the middle layer of a three layer elastic medium. The DDs are assumed to be normal to the two parallel interfaces between the leastic media, and solutions will be presented for both 2D and 3D elastic media. Using the Fourier transform (FT) method we construct the leading term in the asymptotic expansion for the spectral coefficient functions for a DD in a three layer medium. Although a closed form solution will require an infinite series solution, we demonstrate how this UAS can be used to construct highly efficient and accurate solutions even in the case in which the DD actually touches the interface. We present an explicit UAS for elements in which the DD fields are assumed to be piecewise constant throughout a line segment in 2D and a rectangular element in 3D. We demonstrate the usefulness of this UAS by providing a number of examples in which the UAS is used to solve problems in which cracks just touch or cross an interface. The accuracy and efficiency of the algorithm is demonstrated and compared with other numerical methods such as the finite element method and the boudary integral method.     

采用均匀局部二元模式及稀疏表示的掌纹识别

针对传统掌纹识别方法易受噪声干扰,且旋转鲁棒性差的问题,提出一种采用均匀局部二元模式(Uniform Local Binary Patterns,ULBP)及稀疏表示的掌纹识别方法。该方法利用善于表达图像纹理特征,且具有良好旋转不变性和抗干扰性的ULBP提取掌纹图像特征;同时考虑到直接对整幅图像进行ULBP处理会丢失局部纹理,采用先对各图像进行分块,再对各块分别进行ULBP处理的特征提取方案。在分类算法的设计上,本文利用掌纹图像库中训练样本的ULBP特征构造过完备字典,通过求解l1范数意义下的最优化问题实现测试样本的稀疏分解,并提出一种基于统计残差平均的稀疏表示分类方法,实现了测试掌纹图像的分类识别。实验结果表明,本文方法不仅具有良好的旋转及噪声鲁棒性,而且总体识别率明显优于基于PCA及2DPCA的传统稀疏表示分类方法,对于包含5 000031 0人的掌纹数据库,识别率分别提高了8.8%和6.8%。     

On New Perfect Binary Nonlinear Codes

 We present a new construction of binary nonlinear perfect codes with minimum distance 3 and lowerbound the number of nonequivalent such codes. Received: November 26, 1996; revised version: March 14, 1997     

Invariant manifolds and control of hyperbolic trajectories on infinite- or finite-time intervals

We consider general non-autonomous systems on infinite- and finite-time intervals and describe some properties of hyperbolic trajectories and their stable and unstable manifolds. Our definitions of hyperbolic trajectories and their stable and unstable manifolds on finite-time intervals are different from one adopted in the previous references, but still possess a desirable property as the previous one. Furthermore, we present numerical methods based on these theoretical results to compute the stable and unstable manifolds, and propose a control method to stabilize unstable hyperbolic trajectories using geometrical structures near them like the Ott, Grebogi and Yorke (OGY) chaos control method. To demonstrate our methods, we give numerical computation results for two examples: a controlled pendulum on infinite- and finite-time intervals and a simple model for a spacecraft transferring from the Earth to the Moon.     

论远程高等教育的现代化与现代性

远程高等教育现代化既是个自然的历史发展过程，也是个主动创造的过程，它在不断消除距离障碍中重构自我。远程高等教育的现代性表现为：凝聚现代教育理念、创建现代教育结构、重视交互与对话；在后现代主义的影响下，其现代性从思想观念、制度结构和资源技术等方面不断增长。远程高等教育的现代化与现代性既有联系，又有区别。     

Hyper-Kloosterman Sums and their Applications to the Coding Theory

The dual code of the Melas code is called the Kloosterman code. The weights of its codewords can be expressed by the Kloosterman sums, and are uniformly distributed with respect to the Sato-Tate measure. In this paper, the hyper-Kloosterman code C _m (q), a generalization of the Kloosterman code is defined, and the uniform distribution property is deduced using the hyper-Kloosterman sums when m is even and p− 1|m. Finally we discuss doubly-evenness for the weights in the binary case. It shows that we can construct infinitely many doubly-even codes in a non-trivial way. Received: October 30, 2000; revised version: February 28, 2001