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...
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| Дата: | 2018 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| 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| _version_ | 1856543041596162049 |
|---|---|
| author | Dutra, Flaviana S. Ferraz, Raul A. Milies, C. Polcino |
| author_facet | Dutra, Flaviana S. Ferraz, Raul A. Milies, C. Polcino |
| author_sort | Dutra, Flaviana S. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T08:43:10Z |
| description | 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. |
| first_indexed | 2025-12-02T15:41:00Z |
| format | Article |
| id | admjournalluguniveduua-article-785 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:41:00Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-7852018-04-04T08:43:10Z Semisimple group codes and dihedral codes Dutra, Flaviana S. Ferraz, Raul A. Milies, C. Polcino group code, minimal code, group algebra, idempotent, dihedral group, quaternion group 94B15, 94B60, 16S34, 20C05 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. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/785 Algebra and Discrete Mathematics; Vol 8, No 3 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/785/315 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | group code minimal code group algebra idempotent dihedral group quaternion group 94B15 94B60 16S34 20C05 Dutra, Flaviana S. Ferraz, Raul A. Milies, C. Polcino Semisimple group codes and dihedral codes |
| title | Semisimple group codes and dihedral codes |
| title_full | Semisimple group codes and dihedral codes |
| title_fullStr | Semisimple group codes and dihedral codes |
| title_full_unstemmed | Semisimple group codes and dihedral codes |
| title_short | Semisimple group codes and dihedral codes |
| title_sort | semisimple group codes and dihedral codes |
| topic | group code minimal code group algebra idempotent dihedral group quaternion group 94B15 94B60 16S34 20C05 |
| topic_facet | group code minimal code group algebra idempotent dihedral group quaternion group 94B15 94B60 16S34 20C05 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/785 |
| work_keys_str_mv | AT dutraflavianas semisimplegroupcodesanddihedralcodes AT ferrazraula semisimplegroupcodesanddihedralcodes AT miliescpolcino semisimplegroupcodesanddihedralcodes |