Bounds on the Probability of Undetected Error for q-Ary Codes

We study the probability of an undetected error for general q-ary codes. We give upper and lower bounds on this quantity, by the Linear Programming and the Polynomial methods, as a function of the length, size, and minimum distance. Sharper bounds are obtained in the important special case of binary...

Descripción completa

Detalles Bibliográficos
Autores principales: Wang, Xuan, Liu, Huizhou, Solé, Patrick
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10528156/
https://www.ncbi.nlm.nih.gov/pubmed/37761648
http://dx.doi.org/10.3390/e25091349
_version_ 1785111230570037248
author Wang, Xuan
Liu, Huizhou
Solé, Patrick
author_facet Wang, Xuan
Liu, Huizhou
Solé, Patrick
author_sort Wang, Xuan
collection PubMed
description We study the probability of an undetected error for general q-ary codes. We give upper and lower bounds on this quantity, by the Linear Programming and the Polynomial methods, as a function of the length, size, and minimum distance. Sharper bounds are obtained in the important special case of binary Hamming codes. Finally, several examples are given to illustrate the results of this paper.
format Online
Article
Text
id pubmed-10528156
institution National Center for Biotechnology Information
language English
publishDate 2023
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-105281562023-09-28 Bounds on the Probability of Undetected Error for q-Ary Codes Wang, Xuan Liu, Huizhou Solé, Patrick Entropy (Basel) Article We study the probability of an undetected error for general q-ary codes. We give upper and lower bounds on this quantity, by the Linear Programming and the Polynomial methods, as a function of the length, size, and minimum distance. Sharper bounds are obtained in the important special case of binary Hamming codes. Finally, several examples are given to illustrate the results of this paper. MDPI 2023-09-17 /pmc/articles/PMC10528156/ /pubmed/37761648 http://dx.doi.org/10.3390/e25091349 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Wang, Xuan
Liu, Huizhou
Solé, Patrick
Bounds on the Probability of Undetected Error for q-Ary Codes
title Bounds on the Probability of Undetected Error for q-Ary Codes
title_full Bounds on the Probability of Undetected Error for q-Ary Codes
title_fullStr Bounds on the Probability of Undetected Error for q-Ary Codes
title_full_unstemmed Bounds on the Probability of Undetected Error for q-Ary Codes
title_short Bounds on the Probability of Undetected Error for q-Ary Codes
title_sort bounds on the probability of undetected error for q-ary codes
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10528156/
https://www.ncbi.nlm.nih.gov/pubmed/37761648
http://dx.doi.org/10.3390/e25091349
work_keys_str_mv AT wangxuan boundsontheprobabilityofundetectederrorforqarycodes
AT liuhuizhou boundsontheprobabilityofundetectederrorforqarycodes
AT solepatrick boundsontheprobabilityofundetectederrorforqarycodes

Ejemplares similares