Constructing Error-correcting Binary Codes Using Transitive Permutation Groups

Laaksonen Antti, Östergård Patric R. J.. Arxiv 2016

[Paper]    
ARXIV

Let $A_2(n,d)$ be the maximum size of a binary code of length $n$ and minimum distance $d$. In this paper we present the following new lower bounds: $A_2(18,4)\ge 5632$, $A_2(21,4)\ge 40960$, $A_2(22,4)\ge 81920$, $A_2(23,4)\ge 163840$, $A_2(24,4)\ge 327680$, $A_2(24,10)\ge 136$, and $A_2(25,6)\ge 17920$. The new lower bounds are a result of a systematic computer search over transitive permutation groups.

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