English

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 M12M_{12} 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}
}
R2 v1 2026-06-22T14:26:10.190Z