Extended binary Golay codes by a group algebra

• Date: 2024
• Main Authors: Bortos, Maria Yu., Tylyshchak, Alexander A., Khymynets, Myroslava V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2024
• Subjects: group algebra; extended binary codes; Golay codes; self-dual codes; codes over fields; 22D20; 94B05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2241
• Journal Title: Algebra and Discrete Mathematics

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...