作者： Liu,Zihui¹; （¹Key Laboratory of Mathematical Theory and Computation in Information Security, Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China）

出处： Advances in Mathematics of Communications 2024 Vol.18 No.1 P91-104

摘要： We define the generalized Galois inner product for codes over Frobenius rings, and then present the Galois linear complementary dual (LCD) codes over ...

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 P1

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 ...

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 Vol.17 No.3 P306-323

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： Liu, Zihui¹; （¹ Beijing Inst Technol, Dept Math, Key Lab Math Theory & Computat Informat Secur, Beijing 100081, Peoples R China.）

出处： DISCRETE MATHEMATICS 2022 Vol.345 No.5

关键词： GENERALIZED HAMMING WEIGHTS; TRELLIS COMPLEXITY; LENGTH PROFILES; LINEAR CODES

摘要： The descriptions of generalized Hamming weights with respect to rank are given for codes over chain rings. Based on the descriptions of generalized Ha ...

作者： Luo, Yu¹; Liu, Zihui² （¹Department of Mathematics, Beijing Institute of Technology, Beijing, China;²Department 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 2022 P1-1

作者： Wei, Yao¹; Liu, Zihui² （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 2022

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 P1

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 Vol.178 P106298

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： 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 Vol.9 No.2 P181-197

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： 刘义伟 （导师：刘子辉）

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 ...