Decoding the Mathieu group \(M_{12}\) (Q2470821)

The authors consider the sporadic Mathieu group \(M_{12}\) which acts sharply 5-transitively on 12 points. This group is of interest from the point of view of coding theory since it produces a code that is roughly comparable to Reed-Solomon codes over \(\mathbb F_{11}\) and \(\mathbb F_{13}\) in terms of the length, number of codewords and minimum distance. The aim of the authors is to investigate the properties of this group as a code and to determine completely the probabilities of successful and ambiguous decoding of words with more than 3 errors, as \(M_{12}\) has minimum distance 8.