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November  2007, 1(4): 477-487. doi: 10.3934/amc.2007.1.477

Decoding the Mathieu group M12

Robert F. Bailey 1, and  John N. Bray 2,

1. 

School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada
2. 

School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, United Kingdom

Received  June 2007 Revised  October 2007 Published  October 2007

The sporadic Mathieu group M12 can be viewed as an error-correcting code, where the codewords are the group's elements written as permutations in list form, and with the usual Hamming distance. We investigate the properties of this group as a code, in particular determining completely the probabilities of successful and ambiguous decoding of words with more than 3 errors (which is the number that can be guaranteed to be corrected).
Keywords: Permutation code, Mathieu group M12..
Mathematics Subject Classification: Primary: 94B60; Secondary: 20D08, 94B2.
Citation: Robert F. Bailey, John N. Bray. Decoding the Mathieu group M12. Advances in Mathematics of Communications, 2007, 1 (4) : 477-487. doi: 10.3934/amc.2007.1.477
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