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

被引：0
|
作者：
Wang, Xuan [1 ]
Liu, Huizhou [2 ]
Sole, Patrick [3 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China
[2] State Grid Anhui Elect Power Co Ltd, Hefei 230601, Peoples R China
[3] Aix Marseille Univ, CNRS, I2M, Cent Marseille, F-13009 Marseilles, France
来源：
ENTROPY | 2023年 / 25卷 / 09期
关键词：
error correcting codes; probability of undetected error; linear programmming; DISTANCE DISTRIBUTION; BINOMIAL MOMENTS; PROPER;
D O I：
10.3390/e25091349
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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.
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页数：17
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