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Extended binary Golay codes by a group algebra
We study the construction of extended binary Golay codes with respect to the principle (left) ideals of the group algebra \(\mathbb{F}_2G\) of a group \(G\) of order 24 over a field of two elements \(\mathbb{F}_2\). All elements of \(v\in \mathbb{F}_2G\), which generate the principle ideals that def...
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Lugansk National Taras Shevchenko University
2024
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oai:ojs.admjournal.luguniv.edu.ua:article-22412024-09-23T09:29:11Z Extended binary Golay codes by a group algebra Bortos, Maria Yu. Tylyshchak, Alexander A. Khymynets, Myroslava V. group algebra, extended binary codes, Golay codes, self-dual codes, codes over fields 22D20, 94B05 We study the construction of extended binary Golay codes with respect to the principle (left) ideals of the group algebra \(\mathbb{F}_2G\) of a group \(G\) of order 24 over a field of two elements \(\mathbb{F}_2\). All elements of \(v\in \mathbb{F}_2G\), which generate the principle ideals that define extended binary Golay codes, have been found programmatically. Lugansk National Taras Shevchenko University 2024-09-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2241 10.12958/adm2241 Algebra and Discrete Mathematics; Vol 38, No 1 (2024) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2241/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2241/1168 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2241/1239 Copyright (c) 2024 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2024-09-23T09:29:11Z |
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OJS |
| language |
English |
| topic |
group algebra extended binary codes Golay codes self-dual codes codes over fields 22D20 94B05 |
| spellingShingle |
group algebra extended binary codes Golay codes self-dual codes codes over fields 22D20 94B05 Bortos, Maria Yu. Tylyshchak, Alexander A. Khymynets, Myroslava V. Extended binary Golay codes by a group algebra |
| topic_facet |
group algebra extended binary codes Golay codes self-dual codes codes over fields 22D20 94B05 |
| format |
Article |
| author |
Bortos, Maria Yu. Tylyshchak, Alexander A. Khymynets, Myroslava V. |
| author_facet |
Bortos, Maria Yu. Tylyshchak, Alexander A. Khymynets, Myroslava V. |
| author_sort |
Bortos, Maria Yu. |
| title |
Extended binary Golay codes by a group algebra |
| title_short |
Extended binary Golay codes by a group algebra |
| title_full |
Extended binary Golay codes by a group algebra |
| title_fullStr |
Extended binary Golay codes by a group algebra |
| title_full_unstemmed |
Extended binary Golay codes by a group algebra |
| title_sort |
extended binary golay codes by a group algebra |
| description |
We study the construction of extended binary Golay codes with respect to the principle (left) ideals of the group algebra \(\mathbb{F}_2G\) of a group \(G\) of order 24 over a field of two elements \(\mathbb{F}_2\). All elements of \(v\in \mathbb{F}_2G\), which generate the principle ideals that define extended binary Golay codes, have been found programmatically. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2024 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2241 |
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AT bortosmariayu extendedbinarygolaycodesbyagroupalgebra AT tylyshchakalexandera extendedbinarygolaycodesbyagroupalgebra AT khymynetsmyroslavav extendedbinarygolaycodesbyagroupalgebra |
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2024-09-24T04:03:45Z |
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2024-09-24T04:03:45Z |
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1820651918410645504 |