Advances in Mathematics of Communications (AMC)

Decoding the Mathieu group M12

Pages: 477 - 487, Volume 1, Issue 4, November 2007      doi:10.3934/amc.2007.1.477

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Robert F. Bailey - School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada (email)
John N. Bray - School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, E1 4NS, United Kingdom (email)

Abstract: 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, 94B25.

Received: June 2007;      Revised: October 2007;      Available Online: October 2007.