Niederreiter-Rosenbloom-Tsfasman LCD codes

Xu, Heqian; Xu, Guanghan; Du, Wei

doi:10.3934/amc.2022065

Cited by 3 publications

(4 citation statements)

References 28 publications

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“…Niederreiter-Rosenbloom-Tsfasman linear complementary dual (NRT-LCD) codes were defined in [7]. In order to study NRT-LCD codes, we introduce the following definitions.…”

Section: Niederreiter-rosenbloom-tsfasman Lcd Codesmentioning

confidence: 99%

“…Niederreiter-Rosenbloom-Tsfasman Linear complementary dual codes were characterized in terms of generator matrix by Heqian, Guangkui, and Wei in [7].…”

Section: Niederreiter-rosenbloom-tsfasman Lcd Codesmentioning

confidence: 99%

“…Recently, Heqian, Guangkui, and Wei defined NRT-LCD codes in [7]. In the same paper, the basic conditions for an NRT metric code be NRT-LCD are studied.…”

Section: Introductionmentioning

confidence: 99%

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Bounds on Binary Niederreiter-Rosenbloom-Tsfasman LCD codes

Santos¹

2023

Preprint

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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 Mn,s(Fq). 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 M1,s(F2). We present a linear programming bound for binary NRT-LCD codes in Mn,2(F2). We also give two methods to construct binary NRT-LCD codes.

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“…Niederreiter-Rosenbloom-Tsfasman linear complementary dual (NRT-LCD) codes were defined in [7]. In order to study NRT-LCD codes, we introduce the following definitions.…”

Section: Niederreiter-rosenbloom-tsfasman Lcd Codesmentioning

confidence: 99%

“…Niederreiter-Rosenbloom-Tsfasman Linear complementary dual codes were characterized in terms of generator matrix by Heqian, Guangkui, and Wei in [7].…”

Section: Niederreiter-rosenbloom-tsfasman Lcd Codesmentioning

confidence: 99%

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Bounds on Binary Niederreiter-Rosenbloom-Tsfasman LCD codes

Santos¹

2023

Preprint

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“…Since its introduction, the Rosenbloom-Tsfasman metric has spurred numerous investigations into various coding-theoretic questions. Researchers have explored bounds [1,18], weight distribution, MacWilliams identities [4,24,26], self-dual codes [13,22], LCD codes [29], MDS codes [5,6,27], and burst error enumeration [11,25]. These investigations have contributed to a deeper understanding of coding theory in the context of Rosenbloom-Tsfasman metrics.…”

mentioning

confidence: 99%

Fractional decoding and the Rosenbloom-Tsfasman metric

Santos

2024

AMC

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In this paper, we consider the problem of recovering data from partial information considering array codes in the metric space M l,n (Fq) endowed with the Rosenbloom-Tsfasman metric (RT-metric), which are called RT array codes. To be more precise, we want to recover the original data from a received word under the constraint that the decoder can download only an α proportion of the received word. This is called fractional decoding.We show that for any (n, k, l) maximum RT distance separable array code, it is possible to utilize just an α-proportion of the received corrupted codeword to decoding without losing the RT-error correcting capability. Furthermore, we introduce a novel probabilistic fractional decoding algorithm designed to handle random errors. This new algorithm exhibits the ability to correct a larger number of errors compared to the α-decoding radius of (n, k, l) MDS Hamming metric array codes.

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Reversible codes in the Rosenbloom-Tsfasman metric

Gopinadh,

Marka

2024

MATH

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<p>Reversible codes have a range of wide applications in cryptography, data storage, and communication systems. In this paper, we investigated reversible codes under the Rosenbloom-Tsfasman metric (RT-metric). First, some properties of reversible codes in the RT-metric were described. An essential condition for a reversible code to be a maximum distance separable code (MDS code, in short) in the RT-metric was established. A necessary condition for a binary self-dual code to be reversible was proven and the same was generalized for $ q $-ary self-dual reversible codes. Several constructions for reversible RT-metric codes were provided in terms of their generator matrices.</p>

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Niederreiter-Rosenbloom-Tsfasman LCD codes

Cited by 3 publications

References 28 publications

Bounds on Binary Niederreiter-Rosenbloom-Tsfasman LCD codes

Bounds on Binary Niederreiter-Rosenbloom-Tsfasman LCD codes

Fractional decoding and the Rosenbloom-Tsfasman metric

Reversible codes in the Rosenbloom-Tsfasman metric

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