Linear complementary dual codes (LCD codes) are codes whose intersections with their dual codes are trivial. These codes were introduced by Massey in 1992. LCD codes have wide applications in data storage, communication systems, and cryptography. Niederreiter-Rosenbloom-Tsfasman LCD codes (NRT-LCD codes) were introduced by Heqian, Guangku and Wei as a generalization of LCD codes for the NRT metric space $M_{n,s}(\mathbb{F}_{q})$. In this paper, we study LCD$[n\times s,k]$, the maximum minimum NRT distance among all binary $[n\times s,k]$ NRT-LCD codes. We prove the existence (non-existence) of binary maximum distance separable NRT-LCD codes in $M_{1,s}(\mathbb{F}_{2})$. We present a linear programming bound for binary NRT-LCD codes in $M_{n,2}(\mathbb{F}_{2})$. We also give two methods to construct binary NRT-LCD codes.

翻译：线性互补对偶码（LCD码）是指与其对偶码交集中仅包含零码字的码。这类码由Massey于1992年引入，在数据存储、通信系统和密码学中具有广泛应用。Niederreiter-Rosenbloom-Tsfasman LCD码（NRT-LCD码）由Heqian、Guangku和Wei提出，是NRT度量空间$M_{n,s}(\mathbb{F}_{q})$中LCD码的推广。本文研究LCD$[n\times s,k]$——所有二进制$[n\times s,k]$ NRT-LCD码的最大最小NRT距离。我们证明了$M_{1,s}(\mathbb{F}_{2})$中二进制最大距离可分NRT-LCD码的存在性与不存在性，给出了$M_{n,2}(\mathbb{F}_{2})$中二进制NRT-LCD码的线性规划界，并提出了两种构造二进制NRT-LCD码的方法。