Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space with mixed binary and quaternary alphabets. These codes are additive, in the sense that they are additive subgroups, rather than linear as they are not vector spaces over some finite field. We study the structure of these codes and we use the canonical Gray map from this space to the Hamming space to construct binary LCD codes in certain cases. We give examples of such binary LCD codes which are distance-optimal, i.e., they have the largest minimum distance among all binary LCD codes with the same length and dimension.

线性互补对偶代码由Massey在1992年定义，并用于为两个用户二进制加法器通道提供最佳线性编码解决方案。在本文中，我们使用混合的二进制和四进制字母定义环境空间中LCD编码的模拟。从它们是加性子组的意义上说，这些代码是加性的，而不是线性的，因为它们不是某个有限域上的向量空间。我们研究了这些代码的结构，并在某些情况下使用了从该空间到汉明空间的规范格雷图来构造二进制LCD代码。我们给出这种距离最佳的二进制LCD代码的示例，即，它们在具有相同长度和尺寸的所有二进制LCD代码中具有最大的最小距离。