A binary triply-even $[98280, 25, 47104]_2$ code invariant under the sporadic simple group ${\rm Co}_1$ is constructed by adjoining the all-ones vector to the faithful and absolutely irreducible 24-dimensional code of length 98280. Using the action of ${\rm Co}_1$ 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 ${\rm Co}_1$. Moreover, we give a partial description of the nature of the codewords of minimum weight of the dual code.
Rodrigues, B. (2022). On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$. International Journal of Group Theory, 11(1), 23-35. doi: 10.22108/ijgt.2021.123705.1632
MLA
Bernardo G. Rodrigues. "On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$". International Journal of Group Theory, 11, 1, 2022, 23-35. doi: 10.22108/ijgt.2021.123705.1632
HARVARD
Rodrigues, B. (2022). 'On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$', International Journal of Group Theory, 11(1), pp. 23-35. doi: 10.22108/ijgt.2021.123705.1632
VANCOUVER
Rodrigues, B. On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$. International Journal of Group Theory, 2022; 11(1): 23-35. doi: 10.22108/ijgt.2021.123705.1632
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