On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$
| Autor: | Bernardo Rodrigues |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | International Journal of Group Theory, Vol 11, Iss 1, Pp 23-35 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2251-7650 2251-7669 76214184 |
| DOI: | 10.22108/ijgt.2021.123705.1632 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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