On the number of error correcting codes

被引：1
|
作者：
Dong, Dingding [1 ]
Mani, Nitya [2 ]
Zhao, Yufei [2 ]
机构：
[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA
[2] MIT, Dept Math, Cambridge, MA 02139 USA
来源：
COMBINATORICS PROBABILITY AND COMPUTING | 2023年 / 32卷 / 05期
关键词：
error correcting codes; graph theory; containers; CONTAINERS;
D O I：
10.1017/S0963548323000111
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We show that for a fixed q, the number of q-ary t-error correcting codes of length n is at most 2((1+o(1))Hq(n,t)) for all t <= (1 - q(-1))n - 2 root n log n, where H-q(n, t) = q(n)/V-q(n, t) is the Hamming bound and V-q(n, t) is the cardinality of the radius t Hamming ball. This proves a conjecture of Balogh, Treglown, and Wagner, who showed the result for t = o(n(1/3)(log n)(-2/3)).
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页码：819 / 832
页数：14
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