Codes Derived from Binary Goppa Codes

We present a new family of binary codes derived from the family of classical Goppa codes. We generalize properties of Goppa codes to this family, including bounds on the dimension and minimum distance and construction of a polynomial-time algorithm of decoding up to the designed distance. Asymptotically, these codes have the same parameters as Goppa codes.     

On Matrix Rigidity and Locally Self-correctable Codes

We describe a new connection between the problem of finding rigid matrices, as posed by Valiant (MFCS 1977), and the problem of proving lower bounds for linear locally correctable codes. Our result shows that proving linear lower bounds on locally correctable codes with super-logarithmic query complexity will give new constructions of rigid matrices. The interest in constructing rigid matrices is their connection to circuit lower bounds.     

Binary Cyclic Codes and Minimal Codewords

Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal codewords in linear codes are widely used in constructing decoding algorithms and studying linear secret sharing scheme. In this paper, we show that in the binary cyclic code all of the codewords are minimal, except 0 and 1. Then, we obtain a result about the number of minimal codewords in the binary cyclic codes.     

Learning Multifunctional Binary Codes for Personalized Image Retrieval

International Journal of Computer Vision - Due to the highly complex semantic information of images, even with the same query image, the expected content-based image retrieval results could be very...     

基于二进制对称信道的极化码研究

现有极化码构造方案仅适用于二进制删除信道和加性高斯白噪声信道。为此,研究极化码在二进制对称信道(BSC)的构造方案。分析BSC中的极化码构造方式和编译码算法原理,利用连续删除译码算法对极化码在BSC中的纠错效率进行测试。仿真结果表明,蒙特卡罗法构造的极化码相对于巴氏参数法构造的极化码具有较好的纠错效率。     

Binary Perfect Codes of Length 15 by the Generalized Concatenated Construction

We enumerate binary nonlinear perfect codes of length 15 obtained by the generalized concatenated (GC) construction. There are 15 different types of such codes. They are defined by pairs of MDS codes A _i : (4, 2, 64)₄. For every pair we give the number of nonequivalent codes of this type. In total, there are 777 nonequivalent binary perfect codes of length 15 obtained by the GC construction. This number includes the Hamming code (of rank 11), 18 Vasil'ev codes (of rank 12), and 758 codes of rank 13.     

Binary Codes Formed by Functions with Nontrivial Inertia Groups

Let K be a permutation group acting on binary vectors of length n and F _K be a code of length 2 ⁿ consisting of all binary functions with nontrivial inertia group in K. We obtain upper and lower bounds on the covering radii of F _K , where K are certain subgroups of the affine permutation group GA _n . We also obtain estimates for distances between F _K and almost all functions in n variables as n . We prove the existence of functions with the trivial inertia group in GA _n for all n 7. An upper bound for the asymmetry of a k-uniform hypergraph is obtained.     

Binary Extended Perfect Codes of Length 16 by the Generalized Concatenated Construction

We enumerate binary extended nonlinear perfect codes of length 16 obtained by the generalized concatenated construction (GC-construction). There are 15 different types of such codes. They are defined by pairs of MDS codes A _i : (4, 2, 64)₄. For every pair, we give the number of nonequivalent codes of this type. In total, there are 285 nonequivalent binary extended nonlinear perfect codes of length 16 obtained by the GC-construction, including the Hamming (i.e., linear) code. Thus, we obtain all binary extended perfect codes of length 16 and rank 13. Their total number is equal to 272.     

To the Theory of Low-Density Convolutional Codes. II

A theoretical and experimental analysis of iterative decoding of low-density convolutional (LDC) codes is given. Two families are investigated: homogeneous LDC codes and a convolutional code version of turbo-codes.     

基于RS码的二值图像认证及篡改定位算法

用于二值图像内容认证和篡改定位的数字水印技术具有重要的实际价值,但却面临着二值图像像素单一、嵌入容量有限且分布不均匀等问题.根据纠错码--RS码的检错原理,提出一种用于二值图像内容认证和篡改定位的脆弱的数字水印算法.该算法利用二值图像的像素值来构造RS码,通过嵌入其校验码来实现对图像的内容认证和篡改定位,一方面保证了其优越的检错能力;另一方面,具有较低的嵌入负载.经实验证明,该算法能有效地检测出二值图像是否被篡改以及篡改发生的位置.此外,在水印信号的生成和提取过程中使用了密钥,确保了水印的安全.     

基于LabVIEW的调试仪提高测量精度的措施

高精度是变流装置调试仪的重要技术指标,本文针对基于LabVIEW开发的一套双向变流装置调试仪,从硬件和软件两个方面研究分析了影响其精度的主要原因以及提高其测量精度的几项措施,重点讨论了软件措施中的数字滤波和小波处理技术.并结合试验结果进行了验证.     

基于二重结构编码遗传算法求解背包问题的研究

针对背包问题传统的解决方法有动态规划法、分支界限法、回溯法.传统的方法不能有效地解决背包问题.文中提出二重结构编码的遗传算法解决背包问题,是一种适合于在大量的可行解中搜索最优解的有效算法,在约束条件的处理上结合贪婪算法,既加快了算法的收敛速度,又克服了传统方法容易陷入局部最优的特点,提高了搜索效率.通过计算机仿真试验结果表明,二重结构编码的遗传算法比基本遗传编码有更好的近似解,充分证明了使用二重结构编码的混合遗传算法来求解背包问题的有效性和实用性.     

基于有阶为7的自同构的二元双偶编码[56,28,12]的研究

编码纠错、检错是计算机应用中最重要的操作手段之一，双偶编码在其中有着重要作用，但目前对长度较大的编码却研究甚少，尤其在对编码分类问题的研究中遇到较大困难。针对此问题，本文给出了所有有阶为7的自同构的二元极大双偶编码[56，28，12]，在等价关系下有499种这样的编码，从而使这类编码得到彻底解决。     

Structured Learning of Binary Codes with Column Generation for Optimizing Ranking Measures

Hashing methods aim to learn a set of hash functions which map the original features to compact binary codes with similarity preserving in the Hamming space. Hashing has proven a valuable tool for large-scale information retrieval. We propose a column generation based binary code learning framework for data-dependent hash function learning. Given a set of triplets that encode the pairwise similarity comparison information, our column generation based method learns hash functions that preserve the relative comparison relations within the large-margin learning framework. Our method iteratively learns the best hash functions during the column generation procedure. Existing hashing methods optimize over simple objectives such as the reconstruction error or graph Laplacian related loss functions, instead of the performance evaluation criteria of interest—multivariate performance measures such as the AUC and NDCG. Our column generation based method can be further generalized from the triplet loss to a general structured learning based framework that allows one to directly optimize multivariate performance measures. For optimizing general ranking measures, the resulting optimization problem can involve exponentially or infinitely many variables and constraints, which is more challenging than standard structured output learning. We use a combination of column generation and cutting-plane techniques to solve the optimization problem. To speed-up the training we further explore stage-wise training and propose to optimize a simplified NDCG loss for efficient inference. We demonstrate the generality of our method by applying it to ranking prediction and image retrieval, and show that it outperforms several state-of-the-art hashing methods.     

使用DAO访问Access数据表的Binary字段

Ａｃｃｅｓｓ数据具有针对数据库集成性的最优文件结构,其数据表中的Ｂｉｎａｒｙ字段是专为存放二进制数据而设的,在此详尽探讨了ＶＣ５．０中使用ＤＡＯ类访问Ａｃｃｅｓｓ数据中表Ｂｉｎａｒｙ字段的途径及其相关的ＣＯｌｅＶａｒｉｎｎｔ的应用方法。     

一种基于随机序列的数字指纹编码和跟踪算法

基于二进制随机编码技术,提出了一种简洁有效的合谋容忍数字指纹编码和跟踪算法.从理论上推导了算法的编码长度、合谋人数以及跟踪算法错误概率之间的关系,给出了错误概率界.在不同的应用场合,对于给定的任意小的错误概率,可以通过适当选取编码长度,使得在抗一定合谋攻击强度的情况下,错误概率满足应用要求.相对于已有的二进制随机编码指纹算法,在同样的错误概率下,本算法的数字指纹编码长度得到有效缩短.     

Logical Modulo Test Circuits: Their Design in Unitary Positional Binary Codes

Design of logical circuits for modulo tests in unitary parallel binary code is described. The complexity and speed of circuits designed by different methods are evaluated.     

矩形点阵上八近邻图像的链码转换算法

给出了矩形点阵上八近邻图像的顶点链码（VCC）、Freeman链码和边界链码之间的转换算法，给出了图像边界的边界链码与顶点链码之间的相互转化算法和顶点链码与Freeman链码之间的相互转换算法，于是可以方便地直接由一种链码得到其他的链码表示，由某种链码获得的图像信息也为其他链码所共享．