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.