Bounds on the Probability of Undetected Error for <i>q</i>-Ary Codes
We study the probability of an undetected error for general <i>q</i>-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 spe...
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MDPI AG
2023-09-01
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Series: | Entropy |
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Online Access: | https://www.mdpi.com/1099-4300/25/9/1349 |
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author | Xuan Wang Huizhou Liu Patrick Solé |
author_facet | Xuan Wang Huizhou Liu Patrick Solé |
author_sort | Xuan Wang |
collection | DOAJ |
description | We study the probability of an undetected error for general <i>q</i>-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. |
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id | doaj.art-828b55c29e9b43948ca28c37f63e245b |
institution | Directory Open Access Journal |
issn | 1099-4300 |
language | English |
last_indexed | 2024-03-10T22:47:23Z |
publishDate | 2023-09-01 |
publisher | MDPI AG |
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series | Entropy |
spelling | doaj.art-828b55c29e9b43948ca28c37f63e245b2023-11-19T10:36:22ZengMDPI AGEntropy1099-43002023-09-01259134910.3390/e25091349Bounds on the Probability of Undetected Error for <i>q</i>-Ary CodesXuan Wang0Huizhou Liu1Patrick Solé2School of Mathematical Sciences, Anhui University, Hefei 230601, ChinaState Grid Anhui Electric Power Co., Ltd., Hefei 230601, ChinaI2M, CNRS, Aix-Marseille Univetsity, Centrale Marseille, 13009 Marseilles, FranceWe study the probability of an undetected error for general <i>q</i>-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.https://www.mdpi.com/1099-4300/25/9/1349error correcting codesprobability of undetected errorlinear programmming |
spellingShingle | Xuan Wang Huizhou Liu Patrick Solé Bounds on the Probability of Undetected Error for <i>q</i>-Ary Codes Entropy error correcting codes probability of undetected error linear programmming |
title | Bounds on the Probability of Undetected Error for <i>q</i>-Ary Codes |
title_full | Bounds on the Probability of Undetected Error for <i>q</i>-Ary Codes |
title_fullStr | Bounds on the Probability of Undetected Error for <i>q</i>-Ary Codes |
title_full_unstemmed | Bounds on the Probability of Undetected Error for <i>q</i>-Ary Codes |
title_short | Bounds on the Probability of Undetected Error for <i>q</i>-Ary Codes |
title_sort | bounds on the probability of undetected error for i q i ary codes |
topic | error correcting codes probability of undetected error linear programmming |
url | https://www.mdpi.com/1099-4300/25/9/1349 |
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