检索结果-内蒙古大学图书馆

When Does the Extended code of an mds code Remain mds?

IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第1期71卷 263-272页

作者： Wu, Yansheng Ding, Cunsheng Chen, Tingfang Nanjing Univ Posts & Telecommun Sch Comp Sci Nanjing 210023 Peoples R China Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Hong Kong Peoples R China

For a given linear code C of length n over GF(q) and a nonzero vector u in GF(q)(n) , Sun, Ding and Chen defined an extended linear code C(u) of C , which is a generalisation of the classical extended code C(-1) of C and called the second kind of an extended code of C (see Finite Fields Appl., vol. 96, 102401, 2024 and Discrete Math., vol. 347, no. 9, 114080, 2024). They developed some general theory of the extended codes C(u) and studied the extended codes C(u) of several families of linear codes, including cyclic codes, projective two-weight codes, nonbinary Hamming codes, and a family of reversible mds cyclic codes. The objective of this paper is to investigate the extended codes C(u) of mds codes C over finite fields. The main result of this paper is that the extended code C(u) of an mds [n,k] code C remains mds if and only if the covering radius rho(C-perpendicular to)=k and the vector u is a deep hole of the dual code C-perpendicular to . As applications of this main result, an equivalent statement of mds Conjecture is presented, the extended codes of the GRS codes and extended GRS codes are investigated, and the covering radii and some deep holes of several families of mds codes are also determined.

关键词： codes codecs Generators Vectors Linear codes Parity check codes Computer science Reed-Solomon codes Telecommunications Sun Extended code mds code covering radius deep hole GRS code extended GRS code

来源：评论

学校读者我要写书评

暂无评论

mds code Based Ultralightweight Authentication Protocol for RFID System

引用

IEEE ACCESS 2023年 11卷 10563-10577页

作者： Maurya, Pramod Kumar Ghosh, Haradhan Bagchi, Satya Vellore Inst Technol Sch Comp Sci & Engn Vellore 632014 India Natl Inst Technol Durgapur Dept Math Durgapur 713209 India

Privacy and security are central issues in the deployment of an RFID system. It is vulnerable to several attacks, such as replay attacks, location tracking, man-in-middle attack, de-synchronization attack, etc., due to the inherent weaknesses of underlying wireless communications. In order to tackle these privacy and security concerns, this paper presents an ultralightweight authentication protocol based on group homomorphism and maximum distance separable (mds) code. We use group homomorphism properties to make a server lookup table that reduces searching complexity and overcomes scalability issues. We develop an ultralightweight protocol using mds code properties that employs only bit-wise operators. Formal and informal security analysis of the proposed protocol shows that our proposed protocol resists various attacks. In addition, we use automated security protocol verification tools, AVISPA and Scyther, to validate the security features of the proposed protocol. We demonstrate the correctness proof of the proposed protocol using BAN logic. To measure the level of privacy of the proposed protocol, we use two benchmark metrics to simulate the proposed protocol. The performance analysis indicates that the proposed protocol is efficient for a low-cost environment.

关键词： Protocols Security Authentication Privacy Resists Servers Hash functions Radiofrequency identification Homomorphic encryption Authentication protocol anonymity set group homomorphism mds code privacy RFID system security

来源：评论

学校读者我要写书评

暂无评论

Eleven code: A 3-Erasure mds code with Optimize Partial Stripes Writes 1

引用

12th International Symposium on Advanced Parallel Processing Technologies (APPT)

作者： Zhang, Hongwei Wang, Jinsong Lin, Sheng Tianjin Univ Technol Tianjin Peoples R China Tianjin Key Lab Intelligence Comp & Novel Softwar Tianjin Peoples R China Natl Engn Lab Comp Virus Prevent & Control Techno Tianjin Peoples R China

ISBN: (数字)9783319679525

ISBN: (纸本)9783319679525;9783319679518

In this paper, a novel 3-erasure code having advantages of both horizontal and vertical codes is described. Because of its parity construction liking the Greek Numeral XI, so we call it Eleven code. It is an mds code expanded from H-code (an mds code to optimal partial stripe writes in RAID-6) thus it has optimal storage property. To prove the accuracy of this new code's construction, a program also be designed in this paper;We compare Eleven code to Star code and T-code, and it shows that Eleven code reduces partial stripe write cost by up to 18.13% and 14.11%, respectively.

关键词： 3-erasure code mds code Partial stripe write Performance evaluation

来源：评论

学校读者我要写书评

暂无评论

Double Erasures Correcting mds code with Heterogeneous Placement

Double Erasures Correcting MDS Code with Heterogeneous Place...

引用

3rd International Conference on Machine Design and Manufacturing Engineering (ICMDME)

作者： Luo Xun Shen Huan Hunan Normal Univ Coll Math & Comp Sci Changsha Hunan Peoples R China

ISBN: (纸本)9783038351801

One array code scheme is proposed for double erasures correcting. The scheme made use of horizontal and oblique data placements to accommodate parity strips. The scheme can reduce the occurrences of bottlenecks in part due to the oblique placement. The encoding and decoding algorithms can be used in distributed storage. It has been proved that the code with the encoding scheme is mds. It has also been indicated that the decoding scheme is effective for array code (p-1) x (p+ 1) when p is and only is a prime number. Moreover, two placements stripes are not associated with each other, which made it much easier for decoding to tolerate double erasures.

关键词： double erasures correcting array code mds code parity strip

来源：评论

学校读者我要写书评

暂无评论

Image Secret Sharing Based on mds code

Image Secret Sharing Based on MDS Code

引用

International Conference on Big Data and Artificial Intelligence and Software Engineering (ICBASE)

作者： He, Rui Liu, Shanzheng Liu, Longxiang Geng, Wei Tang, Dan Chengdu Univ Informat Technol Sch Software Engn Chengdu 610225 Sichuan Peoples R China Software Engn Technol Res Support Ctr Informatiza Chengdu Sichuan Peoples R China

ISBN: (纸本)9781728196190

Most of the current Shamir image secret sharing schemes are based on Lagrange interpolation, which uses interpolation polynomials to split and reconstruct the secret. There are some problems, such as high time complexity, low computational efficiency and insufficient utilization of shadow image. To solve the problem of appeal, the proposed scheme combines the bit matrix of mds code to replace the original Lagrange interpolation method. Experimental results show that, in addition to the advantages of most current Lagrange-based interpolation schemes, this scheme does not increase the size of shared images and reduces the computational time complexity, accurately recovers the original secret images, and can be extended to audio and video data, so it is perfect.

关键词： Image Secret Sharing mds code Bit Matrix Shadow Image

来源：评论

学校读者我要写书评

暂无评论

mds codes over F₉ related to the temary Golay code

引用

DISCRETE MATHEMATICS 2004年第1-3期282卷 233-237页

作者： Araya, M Harada, M Yamagata Univ Dept Math Sci Yamagata 9908560 Japan Shizuoka Univ Dept Comp Sci Hamamatsu Shizuoka 4328011 Japan

Goldberg constructed an mds code over F-9 whose ternary image is the ternary Golay [12,6,6] code. Motivated by the work, in this paper, we found all such mds codes over F-9 under some equivalence. (C) 2004 Elsevier B.... 详细信息

关键词： mds code ternary golay code code over F-9

来源：评论

学校读者我要写书评

暂无评论

Characterizations of Nmds codes and a proof of the Geng-Yang-Zhang-Zhou conjecture

引用

FINITE FIELDS AND THEIR APPLICATIONS 2025年 105卷

作者： Qiang, Shiyuan Wei, Huakai Hong, Shaofang Sichuan Univ Math Coll Chengdu 610064 Peoples R China

Let Fq be the finite field of q elements, where q = pm with p being a prime number and m being a positive integer. Let C(q,n,delta,h) be a class of BCH codes of length nand designed distance delta. A linear code Cis said to be maximum distance separable (mds) if the minimum distance d = n - k + 1. If d = n - k, then Cis called an almost mds (Amds) code. Moreover, if both of C and its dual code C perpendicular to are Amds, then Cis called a near mds (Nmds) code. In [9], Geng, Yang, Zhang and Zhou proved that the BCH code C(q,q+1,3,4) is an almost mds code, where q = 3m and m is an odd integer, and they also showed that its parameters is [q + 1, q - 3, 4]. Furthermore, they proposed a conjecture stating that the dual code C perpendicular to (q,q+1,3,4) is also an Amds code with parameters [q + 1, 4, q - 3]. In this paper, we introduce the concept of subset code and use it together with the MacWilliams identity to establish characterizations for the dual code of an Amds code to be an Amds code. Then by this criteria, we show that the Geng-Yang-Zhang-Zhou conjecture is true. Our result together with the Geng-Yang-Zhang-Zhou theorem implies that the BCH code C(q,q+1,3,4) is an Nmds code. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Cyclic code MacWilliams identity Linear code mds code BCH code Amds code Nmds code

来源：评论

学校读者我要写书评

暂无评论

New mds codes of non-GRS type and Nmds codes

引用

DISCRETE MATHEMATICS 2025年第5期348卷

作者： Zhi, Yujie Zhu, Shixin Hefei Univ Technol Sch Math Hefei 230601 Peoples R China

Maximum distance separable (mds) and near maximum distance separable (Nmds) codes have been widely used in various fields such as communication systems, data storage, and quantum codes due to their algebraic properties and excellent error-correcting capabilities. This paper focuses on a specific class of linear codes and establishes necessary and sufficient conditions for them to be mds or Nmds. Additionally, we employ the wellknown Schur method to demonstrate that they are non-equivalent to generalized Reed- Solomon codes. (c) 2025 Published by Elsevier B.V.

关键词： mds code Nmds code Schur product Non-GRS

来源：评论

学校读者我要写书评

暂无评论

Decoding Algorithms of Twisted GRS codes and Twisted Goppa codes

引用

IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第2期71卷 1018-1027页

作者： Sun, Huan Yue, Qin Jia, Xue Li, Chengju Nanjing Univ Aeronaut & Astronaut Dept Math Nanjing 211100 Peoples R China State Key Lab Cryptol Beijing 100878 Peoples R China East China Normal Univ Shanghai Key Lab Trustworthy Comp Shanghai 200062 Peoples R China

In this paper, we use extended Euclid's algorithm to propose new decoding algorithms for two classes of maximum distance separable (mds) twisted generalized Reed-Solomon (TGRS) codes of parameters [ n , n - t , t + 1] over F (q) . For even t , the algorithms can correct (t) /(2) errors with time complexity O ( qn ). Moreover, we also give a new decoding algorithm for a class of twisted Goppa codes. For even degree t of a Goppa polynomial, it can also correct (t) /(2) errors, which generalizes a (sic)(t -1)/(2)(sic)-error-correcting decoding algorithm by Sui and Yue (2023).

关键词： codes Decoding Reed-Solomon codes Polynomials codecs Technological innovation Sun Linear codes Public key cryptography Mathematics Twisted generalized Reed-Solomon code twisted Goppa code mds code decoding algorithm

来源：评论

学校读者我要写书评

暂无评论

Around LCD group codes

引用

DESIGNS codeS AND CRYPTOGRAPHY 2025年第4期93卷 889-897页

作者： de la Cruz, Javier Willems, Wolfgang Univ Norte Barranquilla Colombia Otto von Guericke Univ Magdeburg Germany

In this note we answer some questions on LCD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{ LCD }$$\end{document} group codes posed in de la Cruz and Willems (Des codes Cryptogr 86:2065-2073, 2018) and (Vietnam J Math 51:721-729, 2023). Furthermore, over prime fields we determine completely the p-part of the divisor of an LCD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{ LCD }$$\end{document} group code. In addition we present a natural construction of nearly LCD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text{ LCD }$$\end{document} codes.

关键词： Group code LCD code mds code Projective module Almost LCD code Divisor of a code

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：