Bounds on the Probability of Undetected Error for q-Ary Codes-Reference-Cited by-同舟云学术

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

Published:2023-09-17 Issue:9 Volume:25 Page:1349
ISSN:1099-4300
Container-title:Entropy
language:en
Short-container-title:Entropy

Author:

Wang Xuan¹,Liu Huizhou²,Solé Patrick³^ORCID

Affiliation:

1. School of Mathematical Sciences, Anhui University, Hefei 230601, China

2. State Grid Anhui Electric Power Co., Ltd., Hefei 230601, China

3. I2M, CNRS, Aix-Marseille Univetsity, Centrale Marseille, 13009 Marseilles, France

Abstract

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.

Publisher

MDPI AG

Subject

General Physics and Astronomy

Link

https://www.mdpi.com/1099-4300/25/9/1349/pdf

Reference24 articles.

1. A survey on proper codes;Dodunekova;Discret. Appl. Math.,2008

2. MacWilliams, F.J., and Sloane, N.J.A. (1981). The Theory of Error Correcting Codes, Elsevier.

3. Massey, J. (1978, January 18–20). Coding techniques for digital data networks. Proceedings of the International Conference on Information Theory and Systems, NTG-Fachberichte, Berlin, Germany.

4. On the probability of undetected error for linear block codes;Wolf;IEEE Trans. Commun.,1982

5. Concerning a bound on undetected error probability;Hellman;IEEE Trans. Inform. Theory,1976

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