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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Збережено в:
Бібліографічні деталі
Дата:2024
Автори: Bortos, Maria Yu., Tylyshchak, Alexander A., Khymynets, Myroslava V.
Формат: Стаття
Мова:English
Опубліковано: Lugansk National Taras Shevchenko University 2024
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Онлайн доступ:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2241
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Назва журналу:Algebra and Discrete Mathematics

Репозитарії

Algebra and Discrete Mathematics
Опис
Резюме: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.