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)).

引用

页码：819 / 832

页数：14

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