一种三元线性补对偶码的构造方法

黄山; 朱士信; 李锦

doi:10.11999/JEIT211235

一种三元线性补对偶码的构造方法

doi: 10.11999/JEIT211235

黄山^1, ,,
朱士信²,
李锦²

1.
安徽警官职业学院合肥 230031
2.
合肥工业大学数学学院合肥 230601

基金项目: 国家自然科学基金(12171134) ，安徽省高校自然科学重点项目(KJ2021A1469) ，中央高校基本科研业务费专项资金(JZ2022HGTB0264)

详细信息

作者简介:
黄山：女，助教，研究方向为编码理论

朱士信：男，教授，博士生导师，研究方向为编码理论、序列密码与信息安全

李锦：女，副教授，硕士生导师，研究方向为编码理论

通讯作者:
黄山　huangshan5197@163.com

中图分类号: TN911.22
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- 文章访问数: 503
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- PDF下载量: 84
- 被引次数: 0
出版历程
- 收稿日期: 2021-11-08
- 修回日期: 2022-09-01
- 网络出版日期: 2022-09-03
- 刊出日期: 2023-01-17

A Method for Constructing Ternary Linear Complementary Dual Codes

HUANG Shan^{1
, ,},
ZHU Shixin²,
LI Jin²

1.
Anhui Vocational College of Police Officers, Hefei 230031, China
2.
School of Mathematics, Hefei University of Technology, Hefei 230601, China

Funds: The National Natural Science Foundation of China (12171134) , The Key Projects of Natural Science Research of Universities in Anhui Province (KJ2021A1469) , The Fundamental Research Funds of the Central Universties (JZ2022HGTB0264)

摘要

摘要: 线性补对偶(LCD)码在抵御侧信道分析和错误注入攻击方面具有重要应用。该文利用环$ {\mathbb{F}_3} + u{\mathbb{F}_3} $($ {u^2} = 0 $)上线性码，给出一种构造3元LCD码的方法。引入了$ {({\mathbb{F}_3} + u{\mathbb{F}_3})^n} $到$ \mathbb{F}_3^{2n} $的等距Gray映射，给出了环$ {\mathbb{F}_3} + u{\mathbb{F}_3} $上长度为$ n $的线性码的Gray象是3元长度为$ 2n $的LCD码的充分条件，利用环$ {\mathbb{F}_3} + u{\mathbb{F}_3} $上循环码的Gray象，构造了4类参数好的3元LCD码。
- 最优码 /
- 线性补对偶码 /
- 3元码
Abstract: Linear Complementary Dual (LCD) codes have important applications to resisting side-channel analysis and fault-injection attacks. A method is proposed to construct ternary LCD codes by using linear codes over ring $ {\mathbb{F}_3} + u{\mathbb{F}_3} $, where $ {u^2} = 0 $. A Gray map from $ {({\mathbb{F}_3} + u{\mathbb{F}_3})^n} $ to $ \mathbb{F}_3^{2n} $ is introduced, and a sufficient condition for the Gray image of linear codes with length $ n $ over $ {\mathbb{F}_3} + u{\mathbb{F}_3} $ to be ternary LCD codes with length $ 2n $ is given. Four classes of ternary LCD codes with better parameters are constructed via the Gray image of cyclic codes over $ {\mathbb{F}_3} + u{\mathbb{F}_3} $.
- Optimal codes /
- Linear Complementary Dual (LCD) codes /
- Ternary codes

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参考文献(39)

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