Constructing error-correcting binary codes using transitive permutation groups

Antti Laaksonen; Patric R. J. Östergård

paper

Constructing error-correcting binary codes using transitive permutation groups

arXiv:1604.06022

Abstract

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: $A_{2} (18, 4) \geq 5632$ , $A_{2} (21, 4) \geq 40960$ , $A_{2} (22, 4) \geq 81920$ , $A_{2} (23, 4) \geq 163840$ , $A_{2} (24, 4) \geq 327680$ , $A_{2} (24, 10) \geq 136$ , and $A_{2} (25, 6) \geq 17920$ . The new lower bounds are a result of a systematic computer search over transitive permutation groups.