作者：刘义伟

学位名称：硕士

出处：北京理工大学数学与统计学院 2016

关键词：重量分布；迹函数；秘密共享方案；广义汉明重量；高斯和；认证码；完全重量分布；分离性；分离坐标位；相对等重码；支撑重

摘要：最近，通过利用定义集，很多几重量线性码被广泛的构造和研究。这些线性码在秘密共享、认证码和强正则图上都有应用。文章第一部分，推广了王秋燕所构造的线性码，获得了很多新的几重量线性码。这些码的重量分布和它们对偶码的最小距离都被完全确定。文章还证明了这些对偶码集合的一些子类是最优码，并且计算了在一些情况下上 ...

作者：李馨

学位名称：硕士

出处：北京理工大学 2015

摘要：研究内容将以2005年骆源给出的推广的第二类窃密信道为背景,提出相对贪婪重量谱概念。我们将利用有限射影几何方法来等价描述相对贪婪重量谱,通过这种有限射影几何方法,我们能够找到三维q元最优码。这种最优码使得已经窃取到第一位信息的窃密者如果想要获得第二位信息,那么他付出的代价将最大,即窃密者不得不窃听到 ...

作者：Wei, Yao;Liu, Zihui （¹Department of Mathematics, Beijing Institute of Technology, Beijing, China ²Key Laboratory of Mathematical Theory and Computation in Information Security, Department of Mathematics, Beijing Institute of Technology, Beijing, China）

出处：IET Communications (Wiley-Blackwell) 2023

关键词：finite geometry method;relative generalized Hamming weight;relative greedy weight;value assignment

摘要：Motivated by the concepts of the relative generalized Hamming weight and the greedy weight, the relative greedy weight is introduced, and then it is s ...

作者：Wei, Yao;Liu, Zihui （¹Department of Mathematics, Beijing Institute of Technology ²Key Laboratory of Mathematical Theory and Computation in Information Security, Department of Mathematics, Beijing Institute of Technology）

出处：IET Communications (Wiley-Blackwell) 2022

作者：LIAO Da-jian，LIU Yi-wei，LIU Zi-hui，GAO Ying （Department of Mathematics，Huaihai Institute of Technology，Lianyungang，China；Department of Mathematics，Beijing Institute of Technology，Beijing，China；School of Mathematics and Systems Science，Beihang University，Beijing，China）

出处：第二十二届中国电子学会信息论学术年会 2015

摘要：The separating properties of linear q-ary codes(codes over the finite field GF(q))and their applications were first introduced in [9],and then further ...

作者：Li, Xin;Liu, Zihui （¹Beijing Institute of Technology, Department of Mathematics, Beijing, 100081, China, 47833）

出处：Cryptography and communications: discrete structures, Boolean functions and sequences 2017

关键词：Relative greedy weight;Relative generalized Hamming weight;Value assignment;Upper bound;Support weight

摘要：Based on the wire-tap channel of type II with two users given by Luo et al. in 2005, we introduce the relative greedy weights. A finite projective geo ...

作者：Yao Wei¹;Zihui Liu^2,3;CA1 （¹Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China;²Key Laboratory of Mathematical Theory and Computation in Information Security, Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China;³The work is supported by Beijing Natural Science Foundation (No. 1222016) and The National Natural Science Foundation of China (No. 12071027).）

出处：Information Processing Letters 2022

摘要：The relative greedy weights were introduced in 2017 by Li and Liu. We will solve an open problem therein about the second relative greedy weight of 3- ...

作者：Yinghao Liang¹;Zihui Liu²; （¹Department of Mathematics, Beijing Institute of Technology, Beijing, China ²the Department of Mathematics, Key Laboratory of Mathematical Theory and Computation in Information Security, Beijing Institute of Technology, Beijing, China）

出处：IEEE Transactions on Information Theory 2024

关键词：Codes;Vectors;Measurement;Graph theory;Generators;Linear programming;Linear codes

摘要：We present the Plotkin-type bound on the generalized symbol-pair weight and show that all the symbol-pair equiweight codes achieve the Plotkin-type bo ...