Bounds on Binary Niederreiter-Rosenbloom-Tsfasman LCD codes

02/04/2023

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by   Welington Santos, et al.

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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(𝔽_q). In this paper, we study LCD[n× s,k], the maximum minimum NRT distance among all binary [n× s,k] NRT-LCD codes. We prove the existence (non-existence) of binary maximum distance separable NRT-LCD codes in M_1,s(𝔽_2). We present a linear programming bound for binary NRT-LCD codes in M_n,2(𝔽_2). We also give two methods to construct binary NRT-LCD codes.