Título:
On the non-existence of perfect codes in the NRT-metric
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Autor:
Gubitosi, Viviana
Portela, Aldo
Qureshi, Claudio
Portela, Aldo
Qureshi, Claudio
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Tipo de documento:
Preprint
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Palabras clave:
Combinatorics
Information Theory
Information Theory
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Año de publicación:
2023
Contenido:
Resumen:
In this paper we consider codes in Fqs×r with packing radius
R regarding the NRT-metric (i.e. when the underlying poset is a disjoint
union of s chains with the same length r) and we establish necessary
condition on the parameters s, r and R for the existence of perfect codes.
More explicitly, for r, s ≥ 2 and R ≥ 1 we prove that if there is a non-
trivial perfect code then (r+1)(R+1) ≤ rs. We also explore a connection
to the knapsack problem and establish a correspondence between perfect
codes with r > R and those with r = R. Using this correspondence we
prove the non-existence of non-trivial perfect codes also for s = R + 2.
Descripción:
Publicado en arXiv y en IEEE Transactions on Information Theory, vol. 70, no. 6, pp. 4016-4021, June 2024, doi: 10.1109/TIT.2023.3340664, con el título "On the non-existence of perfect codes in the Niederreiter-Rosenbloom-Tsfasman metric".
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Citación:
Gubitosi, V., Portela, A. y Qureshi, C. On the non-existence of perfect codes in the NRT-metric [Preprint] Publicado en : arXiv:2302.11738v2 [math.CO], 2023, pp 1-13. DOI: 10.48550/arXiv.2302.11738. https://arxiv.org/abs/2302.11738.
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Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| GPQ23.pdf | Preprint | 187.11 KB | Adobe PDF |