A ternary [66, 10, 36]3 -code admitting the Mathieu group M12 as a group of auto- morphisms has recently been constructed by N. Pace, see [2]. We give a construction of the Pace code in terms of M12 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.
A combinatorial construction of an M12-invariant code
MARCUGINI, Stefano;PAMBIANCO, Fernanda
2017
Abstract
A ternary [66, 10, 36]3 -code admitting the Mathieu group M12 as a group of auto- morphisms has recently been constructed by N. Pace, see [2]. We give a construction of the Pace code in terms of M12 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.File in questo prodotto:
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