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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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