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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155203 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862701630385815552 |
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| author | Hannusch, C. Lakatos, P. |
| author_facet | Hannusch, C. Lakatos, P. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T16:43:07Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-155203 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T16:43:07Z |
| publishDate | 2016 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Hannusch, C. Lakatos, P. 2019-06-16T10:56:43Z 2019-06-16T10:56:43Z 2016 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. https://nasplib.isofts.kiev.ua/handle/123456789/155203 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. Research of the first author was partially supported by funding of EU’s FP7/2007-2013 grant No. 318202. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes Article published earlier |
| spellingShingle | Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes Hannusch, C. Lakatos, P. |
| title | 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_short | Construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes |
| title_sort | construction of self-dual binary [2²ⁿ,2²ⁿ⁻¹,2ⁿ]-codes |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155203 |
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