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Niederreiter-Rosenbloom-Tsfasman (NRT) code[14]

Description

A poset code based on a partial ordering of \([n]\), i.e., \(1\leq 2\leq \cdots \leq n\).

Protection

LP bounds are provided in Refs. [5,6].

Cousin

Primary Hierarchy

Parents
Niederreiter-Rosenbloom-Tsfasman (NRT) code
Children

References

[1]
H. Niederreiter, “Point sets and sequences with small discrepancy”, Monatshefte für Mathematik 104, 273 (1987) DOI
[2]
H. Niederreiter, “A combinatorial problem for vector spaces over finite fields”, Discrete Mathematics 96, 221 (1991) DOI
[3]
H. Niederreiter, “Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes”, Discrete Mathematics 106–107, 361 (1992) DOI
[4]
M. Yu. Rosenbloom and M. A. Tsfasman, “Codes for the m-Metric”, Problemy Peredachi Informatsii 33(1), 55–63 (1997); Problems of Information Transmission 33(1), 45–52 (1997)
[5]
A. Barg and P. Purkayastha, “Bounds on ordered codes and orthogonal arrays”, (2009) arXiv:cs/0702033
[6]
J. Bierbrauer, “A direct approach to linear programming bounds for codes and tms-nets”, Designs, Codes and Cryptography 42, 127 (2006) DOI
[7]
W. J. Martin and D. R. Stinson, “Association Schemes for Ordered Orthogonal Arrays and (T, M, S)-Nets”, Canadian Journal of Mathematics 51, 326 (1999) DOI
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

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Zoo Code ID: nrt

Cite as:
“Niederreiter-Rosenbloom-Tsfasman (NRT) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/nrt, arXiv:2606.11484
BibTeX:
@incollection{eczoo_nrt,
title={Niederreiter-Rosenbloom-Tsfasman (NRT) code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/nrt}
}
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Permanent link:
https://errorcorrectionzoo.org/c/nrt

Cite as:

“Niederreiter-Rosenbloom-Tsfasman (NRT) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/nrt, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/poset/nrt.yml.