Semisimple group codes and dihedral codes
We consider codes that are given as two-sided ideals in a semisimple finite group algebra \({\mathbb F}_q G\) defined by idempotents constructed from subgroups of \(G\) in a natural way and compute their dimensions and weights. We give a criterion to decide when these ideals are all the minimal two...
Збережено в:
| Дата: | 2018 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/785 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | We consider codes that are given as two-sided ideals in a semisimple finite group algebra \({\mathbb F}_q G\) defined by idempotents constructed from subgroups of \(G\) in a natural way and compute their dimensions and weights. We give a criterion to decide when these ideals are all the minimal two-sided ideals of \({\mathbb F}_q G\) in the case when \(G\) is a dihedral group and extend these results also to a family of quaternion group codes. In the final section, we give a method of decoding; i.e., of finding and correcting eventual transmission errors. |
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