Decoding the Mathieu group M12
|Authors||Robert F. Bailey and John N. Bray.|
|Title||Decoding the Mathieu group M12.|
|Published as||Advances in Mathematics of Communications, to appear.|
|Availability||DVI-format (requires this eps-file too) or PDF-format. Older versions are DVI-format or PDF-format.|
|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).|
A MAGMA program for producing the (interesting) yellow words at distance 7 is here, and a quicker version is here. The resulting 1161 such words are here.
A newer program for determining word colour, and M12 orbits on these words by conjugation is available, and requires this data. The results of this search are available in various files that are readable both by humans and MAGMA.
Finally, this is a link to the La Jolla Covering Repository.
Last updated 26th September 2007|
John N. Bray