Niederreiter-Rosenbloom-Tsfasman LCD codes
Heqian Xu, Guangkui Xu, Wei Du · Advances in Mathematics of Communications · 2022
Linear complementary dual (LCD) codes have wide applications in data storage, communications systems and cryptography. In this paper, we introduce a concept of LCD codes in the metric space \begin{document}$ Mat_{n, s}(\mathbb{F}_{q}) $\end{document} endowed with the Niederreiter-Rosenbloom-Tsfasman metric (NRT metric), which are called Niederreiter-Rosenbloom-Tsfasman LCD (NRT LCD) codes. NRT LCD codes introduced in this paper are actually a generalization of Euclidean LCD codes. For \begin{document}$ s = 1 $\end{document} , an NRT LCD code is just an Euclidean LCD code. A necessary and sufficient condition for an NRT linear code to be an NRT LCD code is provided. Also, the existence of NRT LCD codes is investigated and some constructions of NRT LCD codes and NRT LCD MDS codes are discussed.