Constructing two-weight codes with prescribed groups of automorphisms

We construct new linear two-weight codes over the finite field with q elements. To do so we solve the equivalent problem of finding point sets in the projective geometry with certain intersection properties. These point sets are in bijection to solutions of a Diophantine linear system of equations. To reduce the size of the system of equations we restrict the search for solutions to solutions with special symmetries.Two-weight codes can be used to define strongly regular graphs. We give tables of the two-weight codes and the corresponding strongly regular graphs. In some cases we find new distance-optimal two-weight codes and also new strongly regular graphs.     

关于循环阵列码

本文用代数观点来研究循环阵列码,证明了一般的阵列码是一些极小循环阵列码的直和,并且对极小循环阵列码给出了明确的刻画．当有限域的特征不整除群的阶时,给出了直接写出相应的多项式环的本原幂等元的方法,从而可以直接写出所有的极小循环码．     

Codes Over the p-adic Integers

We study codes over the p-adic integers and correct errors in the existing literature. We show that MDS codes exist over the p-adics for all lengths, ranks and p. We show that self-dual codes exist over the 2-adics if and only if the length is a multiple of 8 and that self-dual codes exist over the p-adics with p odd if and only if the length is 0 (mod 4) for p ≡ 3 (mod 4) and 0 (mod 2) for p ≡ 1 (mod 4).     

On Intersection Problem for Perfect Binary Codes

The main result is that to any even integer q in the interval 0 ≤ q ≤ 2^{n+1-2log(n+1)}, there are two perfect codes C₁ and C₂ of length n = 2^m − 1, m ≥ 4, such that |C₁ ∩ C₂| = q.     

Bounds on Codes Derived by Counting Components in Varshamov Graphs

We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10]     

单层光学薄膜中薄膜－衬底体系的双重干涉效应及其应用

提出了单层光学薄膜中薄膜与衬底反射光之间的双重干涉效应的理论，实验结果证实了理论分析的正确性。双重干涉效应使薄膜－衬底体系的热致反射调制度高达８０％，这一效应可望有极广泛的应用     

一种云存储系统数据持久存储机制

针对云存储中的可靠性产生的担忧,提出一种云存储系统完善的数据存储保障机制,以保证系统的高可靠性和数据的高可用性。在处理与数据持久存储的相关的数据分片、数据分发、完整性检查以及冗余数据的维护中,引入基于纠删码的数据冗余机制,与传统的复制冗余方案相比,能够在获得相同的数据可用性时降低存储空间和网络带宽的开销多达50%以上。采用基于缓冲区的分段读入编码对纠删码算法进行优化后,提高了对文件分片与合并的平均编码速率。     

对偶四元数线阵遥感影像几何定位

提出以对偶四元数为数学工具进行线阵CCD(电荷耦合元件)遥感影像几何定位的全新技术方法。利用对偶四元数建立遥感通用传感器严密成像模型,将光线束的位置和姿态统一用对偶四元数表示,通过传感器扫描光线在空间中的螺旋运动,实现像点到其对应地面点物方坐标的变换,从而克服了成像几何参数(外方位元素)之间的强相关性。按照空间刚体变换线性蒙皮混合理论,可以把刚体变换矩阵分解为平移和旋转两个部分,对平移部分进行线性插值,对旋转部分进行球面插值,从而实现线阵CCD遥感影像外方位元素的解算。按照所建立的成像几何模型,利用某地区Geoeye-1遥感影像进行几何定位实验,实验结果表明新算法获得的几何定位精度优于传统算法,能够解决定位参数之间的相关性问题。     

基于小样本学习的图像分类技术综述

图像分类的应用场景非常广泛, 很多场景下难以收集到足够多的数据来训练模型, 利用小样本学习进行图像分类可解决训练数据量小的问题. 本文对近年来的小样本图像分类算法进行了详细综述, 根据不同的建模方式, 将现有算法分为卷积神经网络模型和图神经网络模型两大类, 其中基于卷积神经网络模型的算法包括四种学习范式: 迁移学习、元学习、对偶学习和贝叶斯学习; 基于图神经网络模型的算法原本适用于非欧几里得结构数据, 但有部分学者将其应用于解决小样本下欧几里得数据的图像分类任务, 有关的研究成果目前相对较少. 此外, 本文汇总了现有文献中出现的数据集并通过实验结果对现有算法的性能进行了比较. 最后, 讨论了小样本图像分类技术的难点及未来研究趋势.