A combinatorial construction of an M_{12}-invariant code
Combinatorics
2016-06-16 v1
Abstract
In this work we summarized some recent results to be included in a forthcoming paper. A ternary [66,10,36]_3-code admitting the Mathieu group M_{12} as a group of automorphisms has recently been constructed by N. Pace. We give a construction of the Pace code in terms of as well as a combinatorial description in terms of the small Witt design, the Steiner system S(5,6,12). We also present a proof that the Pace code does indeed have minimum distance 36.
Keywords
Cite
@article{arxiv.1606.04857,
title = {A combinatorial construction of an M_{12}-invariant code},
author = {Juergen Bierbrauer and Stefano Marcugini and Fernanda Pambianco},
journal= {arXiv preprint arXiv:1606.04857},
year = {2016}
}