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Linear complementary dual codes (LCD codes) are codes whose intersectionswith their dual codes are trivial. These codes were introduced by Massey in1992. 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 forthe NRT metric space $M_{n,s}(\mathbb{F}_{q})$. In this paper, we studyLCD$[n\times s,k]$, the maximum minimum NRT distance among all binary $[n\timess,k]$ NRT-LCD codes. We prove the existence (non-existence) of binary maximumdistance separable NRT-LCD codes in $M_{1,s}(\mathbb{F}_{2})$. We present alinear 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.

Bounds on Binary Niederreiter-Rosenbloom-Tsfasman LCD codes