On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$
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 o...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Isfahan
2022-03-01
|
| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | https://ijgt.ui.ac.ir/article_25586_233dec6d6c4b8c12fde36df763208c3f.pdf |
| _version_ | 1828425951448399872 |
|---|---|
| author | Bernardo Rodrigues |
| author_facet | Bernardo Rodrigues |
| author_sort | Bernardo Rodrigues |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T16:40:03Z |
| format | Article |
| id | doaj.art-187d7621418440dfb5d17c49a72a1b7a |
| institution | Directory Open Access Journal |
| issn | 2251-7650 2251-7669 |
| language | English |
| last_indexed | 2024-12-10T16:40:03Z |
| publishDate | 2022-03-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | International Journal of Group Theory |
| spelling | doaj.art-187d7621418440dfb5d17c49a72a1b7a2022-12-22T01:41:16ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692022-03-01111233510.22108/ijgt.2021.123705.163225586On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$Bernardo Rodrigues0Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Hatfield, Pretoria 0028, South AfricaA 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.https://ijgt.ui.ac.ir/article_25586_233dec6d6c4b8c12fde36df763208c3f.pdfautomorphism groupmodular representationconway group |
| spellingShingle | Bernardo Rodrigues On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$ International Journal of Group Theory automorphism group modular representation conway group |
| title | On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$ |
| title_full | On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$ |
| title_fullStr | On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$ |
| title_full_unstemmed | On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$ |
| title_short | On some projective triply-even binary codes invariant under the Conway group ${\rm Co}_1$ |
| title_sort | on some projective triply even binary codes invariant under the conway group rm co 1 |
| topic | automorphism group modular representation conway group |
| url | https://ijgt.ui.ac.ir/article_25586_233dec6d6c4b8c12fde36df763208c3f.pdf |
| work_keys_str_mv | AT bernardorodrigues onsomeprojectivetriplyevenbinarycodesinvariantundertheconwaygrouprmco1 |