标题： $\mathbb{F}_{2}\mathbb{F}_{4}$-加法互补对偶码 显示英文标题

标题： $\mathbb{F}_{2}\mathbb{F}_{4}$-Additive Complementary Dual Codes

摘要： 在本文中，我们研究了在某种定义于$\mathbb{F}_2\mathbb{F}_4$上的内积下，混合字母表$\mathbb{F}_2\mathbb{F}_4$上的加法互补对偶（ACD）码的结构和性质。我们建立了在这种条件下此类码为加法互补对偶（ACD）码的充分条件。我们还表明，$\mathbb{F}_{2}\mathbb{F}_{4}$上的 ACD 码可以作为线性映射$W$的像来构造二进制线性互补对偶码。值得注意的是，我们证明了如果一个码的二进制像是 LCD，则原码必定是 ACD。给出一个例子，其中图像是一个距离最优的二进制 LCD 码。 显示英文摘要

摘要： In this paper, we investigate the structure and properties of additive complementary dual (ACD) codes over the mixed alphabet $\mathbb{F}_2\mathbb{F}_4$ relative to a certain inner product defined over $\mathbb{F}_2\mathbb{F}_4$. We establish sufficient conditions under which such codes are additive complementary dual (ACD) codes. We also show that ACD codes over $\mathbb{F}_{2}\mathbb{F}_{4}$ can be applied to construct binary linear complementary dual codes as their images under the linear map $W$. Notably, we prove that if the binary image of a code is LCD, then the original code is necessarily ACD. An example is given where the image is a distance-optimal binary LCD code.