二元Niederreiter-Rosenbloom-Tsfasman LCD码的界
Bounds on Binary Niederreiter-Rosenbloom-Tsfasman LCD codes
摘要：
线性互补对偶码（LCD码）是与其对偶码的交集是平凡的码。这些代码由Massey于1992年推出。LCD码在数据存储、通信系统和密码学中有着广泛的应用。Niederreiter-Rosenbloom-Tsfasman LCD码（NRT-LCD码）是由Heqian，Guangku和Wei等人在NRT度量空间$M_{n,s}(\mathbb{F}_{q})$上推广的LCD码。本文研究了所有二进制$[n\times s,k]$ NRT-LCD码中的最大最小NRT距离--LCD码$[n\times s,k]$。证明了在$M_{1,s}(\mathbb{F}_{2})$中二元最大距离可分NRT-LCD码的存在性（不存在性）.本文给出了二进制NRT-LCD码在$M_{n,2}(\mathbb{F}_{2})$中的线性规划界。我们还给出了构造二进制NRT-LCD码的两种方法。
英文摘要：
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.
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