前缀码与极大前缀码的一种新刻画

在语言图Γ(X*)概念的基础上,用新引入的语言竹竿l(X*)和语言竹竿集L(X*)的概念形象地刻画了前缀码与极大前缀码:A是前缀码l(X*)∈L(X*),S_l_((X*))∩A或为单点集或为Φ;A是极大前缀码l(X*)∈L(X*),i)S_(l(X*))∩A或为单点集或为Φ.ii)S_(l(X*))∩A=Φ■u∈S_(l(X*)),■a∈A,ω∈X~+使a=uw.     

On the Hamming distances of repeated-root constacyclic codes of length 4ps

Let $p$ be an odd prime, $s$, $m$ be positive integers, $\gamma ,\lambda$ be nonzero elements of the finite field ${\mathbb{F}}_{p^m}$ such that ${\gamma }^{p^s}=\lambda$. In this paper, we show that, for any positive integer $\eta$, the Hamming distances of all repeated-root $\lambda$-constacyclic codes of length $\eta p^s$ can be determined by those of certain simple-root $\gamma$-constacyclic codes of length $\eta$. Using this result, Hamming distances of all constacyclic codes of length $4p^s$ are obtained. As an application, we identify all MDS $\lambda$-constacyclic codes of length $4p^s$.     

Gray codes extending quadratic matchings

Is it true that every matching in the n-dimensional hypercube can be extended to a Gray code? More than two decades have passed since Ruskey and Savage asked this question and the problem still remains open. A solution is known only in some special cases, including perfect matchings or matchings of linear size. This article shows that the answer to the Ruskey–Savage problem is affirmative for every matching of size at most . The proof is based on an inductive construction that extends balanced matchings in the completion of the hypercube by edges of into a Hamilton cycle of . On the other hand, we show that for every there is a balanced matching in of size that cannot be extended in this way.     

The dual code of any (δ+αu2)-constacyclic code over F2m[u]∕〈u4〉 of oddly even length

Let ${\mathbb{F}}_{2^m}$ be a finite field of cardinality $2^m$, $R={\mathbb{F}}_{2^m}\left[u\right]∕〈u^4〉={\mathbb{F}}_{2^m}+u{\mathbb{F}}_{2^m}+u^2{\mathbb{F}}_{2^m}+u^3{\mathbb{F}}_{2^m}$ $(u^4=0)$ which is a finite chain ring, and $n$ is an odd positive integer. For any $\delta ,\alpha \in {\mathbb{F}}_{2^m}^{\times }$, an explicit representation for the dual code of any $(\delta +\alpha u^2)$-constacyclic code over $R$ of length $2n$ is given. And some dual codes of $(1+u^2)$-constacyclic codes over $R$ of length 14 are constructed. For the case of $\delta =1$, all distinct self-dual $(1+\alpha u^2)$-constacyclic codes over $R$ of length $2n$ are determined.     

基于多尺度结构特征的快速异源图像匹配

针对异源图像提出一种基于多尺度密集结构特征的快速匹配算法。算法首先利用Gabor滤波器逐像素提取图像中的结构响应,再根据主方向响应对多尺度结构特征融合,然后使用快速傅里叶变换在频域计算各特征分量图像之间的卷积,最后将卷积生成的系数矩阵求和计算出图像之间的相似性并选择相似性最大位置作为匹配结果输出。本文算法能有效适应异源图像间的非线性灰度变化和噪声干扰问题。测试使用可见光、红外、雷达图像组成的异源图像数据集对本文算法和现有算法进行测试比较,结果表明:本文算法的平均误匹配率最低,并且计算速度有明显优势。     

Stable blow-up dynamics in the -critical and -supercritical generalized Hartree equation

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, which is a Schrödinger-type equation with a nonlocal, convolution-type nonlinearity: First, we consider the -critical case in dimensions and obtain that a generic blow-up has a self-similar structure and exhibits not only the square root blowup rate , but also the log-log correction (via asymptotic analysis and functional fitting), thus, behaving similarly to the stable blow-up regime in the -critical nonlinear Schrödinger equation. In this setting, we also study blow-up profiles and show that generic blow-up solutions converge to the rescaled , a ground state solution of the elliptic equation . We also consider the -supercritical case in dimensions . We derive the profile equation for the self-similar blow-up and establish the existence and local uniqueness of its solutions. As in the NLS -supercritical regime, the profile equation exhibits branches of nonoscillating, polynomially decaying (multi-bump) solutions. A numerical scheme of putting constraints into solving the corresponding ordinary differential equation is applied during the process of finding the multi-bump solutions. Direct numerical simulation of solutions to the generalized Hartree equation by the dynamic rescaling method indicates that the is the profile for the stable blow-up. In this supercritical case, we obtain the blow-up rate without any correction. This blow-up happens at the focusing level , and thus, numerically observable (unlike the -critical case). In summary, we find that the results are similar to the behavior of stable self-similar blowup solutions in the corresponding settings for the nonlinear Schrödinger equation. Consequently, one may expect that the form of the nonlinearity in the Schrödinger-type equations is not essential in the stable formation of singularities.     

SCMA场景下的极化码编解码方案改进研究

极化码是目前唯一一种被证明可达到信道容量的编码方式,稀疏码分多址接入(Sparse Code Division Multiple Access,SCMA)可以提高频谱资源的利用率和接入系统的用户接入数量。为了提升SCMA与极化码的联合系统的误码率性能和译码时延,使联合系统的应用越来越广泛,提出了2种降低译码复杂度的方式:简化的左信息更新方式和剪枝译码算法。简化的左信息更新方式对于N=256,N=1024的极化码分别能降低37.6%和44.6%的存储资源占用数;剪枝译码算法在码率为0.5时能降低50%左右的计算复杂度。基于简化的SCAN算法改进了联合检测译码算法,在接收机采用外循环迭代的结构,引入了阻尼机制,选取最优的阻尼方式和最优阻尼值。仿真分析了所提联合检测译码算法与原有联合检测译码算法的误码率性能差异,外迭代接收机性能与内外双循环迭代的接收机性能相同,采用阻尼机制联合接收机的性能比无阻尼接收机的性能高0.8 dB左右,SJIDD的误帧率性能比保留宽度为32的SCLJDD的性能低0.7 dB左右,但能使接收机处理时延降至原来的1/4~1/8。