ON SOME PROJECTIVE TRIPLY-EVEN BINARY CODES INVARIANT UNDER THE CONWAY GROUP Co1

A binary triply-even [98280; 25; 47104]2 code invariant under the sporadic simple group Co1 is constructed by adjoining the all-ones vector to the faithful and absolutely irreducible 24-dimensional code of length 98280. Using the action of Co1 on the code we give a description of the nature of the codewords of any non-zero weight relating these to vectors of types 2, 3 and 4, respectively of the Leech lattice. We show that the stabilizer of any non-zero weight codeword in the code is a maximal subgroup of Co1. Moreover, we give a partial description of the nature of the codewords of minimum weight of the dual code.