Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes
The binary Reed-Muller code RM(m−n,m) corresponds to the n-th power of the radical of GF(2)[G], where G is an elementary abelian group of order 2m. Self-dual RM-codes (i.e. some powers of the radical of the previously mentioned group algebra) exist only for odd m. The group algebra approach enables...
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| Дата: | 2016 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2016
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/155203 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes / C. Hannusch, P. Lakatos // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 59-68. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-155203 |
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irk-123456789-1552032019-06-17T01:26:53Z Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes Hannusch, C. Lakatos, P. The binary Reed-Muller code RM(m−n,m) corresponds to the n-th power of the radical of GF(2)[G], where G is an elementary abelian group of order 2m. Self-dual RM-codes (i.e. some powers of the radical of the previously mentioned group algebra) exist only for odd m. The group algebra approach enables us to find a self-dual code for even m=2n in the radical of the previously mentioned group algebra with similarly good parameters as the self-dual RM codes. 2016 Article Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes / C. Hannusch, P. Lakatos // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 59-68. — Бібліогр.: 15 назв. — англ. 1726-3255 2010 MSC:94B05, 11T71, 20C05. http://dspace.nbuv.gov.ua/handle/123456789/155203 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The binary Reed-Muller code RM(m−n,m) corresponds to the n-th power of the radical of GF(2)[G], where G is an elementary abelian group of order 2m. Self-dual RM-codes (i.e. some powers of the radical of the previously mentioned group algebra) exist only for odd m. The group algebra approach enables us to find a self-dual code for even m=2n in the radical of the previously mentioned group algebra with similarly good parameters as the self-dual RM codes. |
| format |
Article |
| author |
Hannusch, C. Lakatos, P. |
| spellingShingle |
Hannusch, C. Lakatos, P. Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes Algebra and Discrete Mathematics |
| author_facet |
Hannusch, C. Lakatos, P. |
| author_sort |
Hannusch, C. |
| title |
Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes |
| title_short |
Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes |
| title_full |
Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes |
| title_fullStr |
Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes |
| title_full_unstemmed |
Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes |
| title_sort |
construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155203 |
| citation_txt |
Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes / C. Hannusch, P. Lakatos // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 59-68. — Бібліогр.: 15 назв. — англ. |
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Algebra and Discrete Mathematics |
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