A Method for Constructing Ternary Linear Complementary Dual Codes
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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。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} $ .-
Key words:
- Optimal codes /
- Linear Complementary Dual (LCD) codes /
- Ternary codes
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