On a signal processing algorithms based class of linear codes

In this work, the correspondence between linear (n,k,d) codes and aperiodic convolution algorithms for computing a system ofk bilinear forms over GF(p^m) is explored. A number of properties are established for the linear codes that can be obtained from a computational procedure of this type. A particular bilinear form is considered and a class of linear codes over GF(2^m) is derived with varyingk andd parameters. The code lengthn is equal to the multiplicative complexity of the computation of an aperiodic convolution and an efficient computation thereof leads to the shortest codes possible using this approach, many of which are optimal or near-optimal. A new decoding procedure for this class of linear codes is presented which exploits the block structure of the generator matrix of the codes. Several interesting observations are made on the nature of the codes obtained as a result of such computations. Such a computation of bilinear forms can be generalized to include other bilinear forms and the related classes of codes.     

A novel approach to generating long low-density parity-check codes using two configurations

A new low-complexity generating method is given for the construction of long low-density parity-check (LDPC) codes. The method is based on performing a combinatorial operation between two given configurations. Combinatorial structures such as lattices, affine and projective planes are considered as the constituent configurations. Using this method, we present several classes of well-structured four-cycle free LDPC codes of high rates most of which are quasi-cyclic. From among the main advantages of this approach, we may refer to its low-complexity property and the fact that from performance perspective the constructed codes compete with the pseudorandom LDPC codes.     

利用酉几何构作新的带仲裁的认证码

利用有限域上酉几何构作一类新的带仲裁的认证码,计算出所构作的码的参数及各种攻击成功的概率。     

Skew-cyclic codes

We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since there are much more skew-cyclic codes, this new class of codes allows to systematically search for codes with good properties. We give many examples of codes which improve the previously best known linear codes.     

List decoding of repeated codes

Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to their parameters, we show that they have a good performance with this algorithm. We compare, by computer simulations, our algorithm for the repeated code of a Reed–Solomon code against a decoding algorithm of a Reed–Solomon code. Finally, we estimate the decoding capability of the algorithm for Reed–Solomon codes and show that performance is somewhat better than our estimates.     

A note on cyclic codes from APN functions

Cyclic codes, as linear block error-correcting codes in coding theory, play a vital role and have wide applications. Ding (SIAM J Discret Math 27(4):1977–1994, 2013), Ding and Zhou (Discret Math, 2014) constructed a number of classes of cyclic codes from almost perfect nonlinear (APN) functions and planar functions over finite fields and presented some open problems on cyclic codes from highly nonlinear functions. In this paper, we consider two open problems involving the inverse APN function $f(x)=x^{q^m-2}$ and the Dobbertin APN function $f(x)=x^{2^{4i}+2^{3i}+2^{2i}+2^{i}-1}$ . From the calculation of linear spans and the minimal polynomials of two sequences generated by these two classes of APN functions, the dimensions of the corresponding cyclic codes are determined and lower bounds on the minimum weight of these cyclic codes are presented. Actually, we present a framework for the minimal polynomial and linear span of the sequence $s^{\infty }$ defined by $s_t={\mathrm {Tr}}((1+\alpha ^t)^e)$ , where $\alpha $ is a primitive element in ${\mathrm {GF}}(q)$ . These techniques can also be applied to other open problems in Ding (SIAM J Discret Math 27(4):1977–1994, 2013), Ding and Zhou (Discret Math, 2014).     

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     

Generalized quasi-cyclic codes: structural properties and code construction

Generalized quasi-cyclic (GQC) codes are defined by generator matrices comprised of circulant matrices of lengths not necessarily identical. A decomposition of these codes is given by using the Chinese reminder theorem. The focus is to characterize ρ-generator GQC codes in details. A good lower bound on the minimum distance of such a code in terms of the minimum distance of the constituent codes is given. Construction methods are given and a set of GQC codes is provided that from minimum distance perspective are optimal codes among the known linear codes having the same length and dimension.     

基于视觉单词和语义映射的色情图像检测算法

针对传统类型的色情图像检测方法误检率高的问题,提出了一种基于多层视觉单词的检测方法.该方法首先对色情场景的各种视觉元素建立视觉单词,然后通过这些视觉单词建立更高层的编码,包括视觉词组和兴趣区域类别,从而实现对图像不同形态级别的描述与分析.图像的识别特征由相应的编码直方图组成,并将特征映射到一个低维空间中,使图像间的语义距离与空间距离相协调.该方法在各种图像测试中都表现出出色的性能,例如在人物类图像测试中,误检率比传统方法降低了40%.实验结果证明,多层单词体系能够更高效地分析色情图像等复杂场景.     

On cyclic codes which areq-ary images of linear codes

This paper presents a complete characterization of cyclic codes over GF(q) which areq-ary images of linear codes over GF(q ²). New cyclic codes over GF(2 ^r ) are constructed as images of other cyclic codes over GF(2^3r ), for some positive integersr. An application to decoding is given.     

Improved parallel weighted bit-flipping decoding algorithm for LDPC codes

Aiming at seeking a low-complexity decoder with fast decoding convergence speed for short or medium low-density parity-check (LDPC) codes, an improved parallel weighted bit-flipping (IPWBF) algorithm, which is applied flexibly for two classes of codes is presented here. For LDPC codes with low column weight in their parity check matrix, both bootstrapping and loop detection procedures, described in the existing literature, are included in IPWBF. Furthermore, a novel delay-handling procedure is introduced to prevent the codeword bits of high reliability from being flipped too hastily. For large column weight finite geometry LDPC codes, only the delay-handling procedure is included in IPWBF to show its effectiveness. Extensive simulation results demonstrate that the proposed algorithm achieves a good tradeoff between performance and complexity.     

Some new binary quasi-cyclic codes from codes over the ring \mathbb F _2+u\mathbb F _2+v\mathbb F _2+uv\mathbb F _2

We consider quasi-cyclic codes over the ring $\mathbb{F }_2+u\mathbb{F }_2+v\mathbb{F }_2+uv\mathbb{F }_2$ , a finite non-chain ring that has been recently studied in coding theory. The Gray images of these codes are shown to be binary quasi-cyclic codes. Using this method we have obtained seventeen new binary quasi-cyclic codes that are new additions to the database of binary quasi-cyclic codes. Moreover, we also obtain a number of binary quasi-cyclic codes with the same parameters as best known binary linear codes that otherwise have more complicated constructions.     

准同步CDMA及其在卫星移动通信中的应用

研究了一种新颖的多址准同步CDMA方式，理论推导了准同步CDMA性能表达式，在性能评价的基础上，构造了两放新的扩频码集，分析表明，采用新码集时，准同步CDMA性能要远优于异步CDMA，最后分析了卫星移动通信系统反向信道采用准同步CDMA时的性能。     

长周期结构相对位移反应谱研究

在对长周期结构进行抗震设计时,或采用基于位移的性能设计方法进行结构设计时,或采用各种结构控制技术对结构进行减隔震设计时,需要用到相对位移反应谱,而目前各国规范给出的一般都是某种标准化的绝对加速度反应谱。本文指出了国内外目前在用的部分规范提出的长周期反应谱存在的问题,采用80条高通低截止频率（0.025~0.125 Hz）、加速度峰值≥0.10 g的水平向强震记录,计算了周期0~10 s、阻尼比0.10~0.40的相对位移反应谱,研究了位移谱的影响因素及控制参数,建立了考虑震源参数、地震动幅值特性、场地条件、谱控制参数、阻尼比调整系数的可供长周期结构设计使用的弹性相对位移谱,给出了实用化计算公式及地震动位移峰值。结果表明,相对位移谱卓越周期是控制位移谱谱值及形状的重要参数;本文研究得到的相对位移谱能较好地拟合实际相对位移谱。     

基于反应力向量灵敏度的模型参数化方法

模型参数化是建立识别方程的关键。本文在虚拟结构向量转换方法的基础上提出了“基于反应力向量灵敏度的模型参数化方法”。该方法首先将反应力向量对单元物理参数作一阶展开，对线性参数系统来说，即为反应力向量灵敏度与单元物理参数的乘积，其次，在线性参数系统的假定下，对一个单元中包含多个单元物理参数的情况提出了一个简便的求反应力向量灵敏度的算法，利用该方法可直接由常规的有限元代码获得反应力向量灵敏度矩阵，而无需仿制专门的有限元代码集成分析代码，文中通过算例阐述了该方法的应用。     

A generalization of justesen codes

Abstract

By using alternant codes as outer codes in the concatenated structure for Justesen codes, a generalization of Justesen codes which completely meets the Zyablov bound is constructed. For this class of codes, the inner codes are explicitly defined while the outer codes are not.     

Covering Radius 1985–1994

 We survey important developments in the theory of covering radius during the period 1985–1994. We present lower bounds, constructions and upper bounds, the linear and nonlinear cases, density and asymptotic results, normality, specific classes of codes, covering radius and dual distance, tables, and open problems. Received October 28, 1994; revised version May 28, 1996     

Onr-partition designs in hamming spaces

The concept of the combinatorial matrix of an unrestricted code and the notion of anr-partition design admitted by a code are introduced and discussed in detail. The theory includes a characterization of completely regular codes, and a combinatorial interpretation of the fact that the distinct rows of the distance distribution matrix of a code are linearly independent. In general, it is possible to compute the distance distribution matrix of any code admitting a given partition design by solving a well-defined system of linear equations; this is an efficient technique provided the number of classes in the partition is relatively small.     

线性隐写码的性质与构造

本文从隐写术的安全性需求出发抽象出一个新的编码问题,称之为隐写码。利用线性空间的直和分解得到了一种线性隐写码的构造方法。通过引入线性空间t阶维数的概念将线性隐写码问题转化成了一个代数问题,从而得到了线性隐写码长度的上界,并由此定义了最大长度可嵌入码。证明了线性最大长度可嵌入码与线性完备纠错码有1-1对应关系。     

A pointwise variational principle for mixed boundary value problems in time harmonic elastodynamics

Stationary functionals are constructed for the displacement field at a specified but arbitrary point, for certain classes of mixed boundary value problems associated with time harmonic linear elastodynamics. The utility of such variational principles is indicated for certain half-space problems with an elliptical line of separation in the boundary conditions.