On semisimple algebra codes: generator theory
The class of affine variety codes is defined as the Fq linear subspaces of A a Fq-semisimple algebra, where Fq is the finite field with q=pr elements and characteristic p. It seems natural to impose to the code some extra structure such as been a subalgebra of A. In this case we will have codes that...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2007 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152365 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On semisimple algebra codes: generator theory / E. Martınez-Moro // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 99–112. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862713549051133952 |
|---|---|
| author | Martınez-Moro, E. |
| author_facet | Martınez-Moro, E. |
| citation_txt | On semisimple algebra codes: generator theory / E. Martınez-Moro // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 99–112. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | The class of affine variety codes is defined as the Fq linear subspaces of A a Fq-semisimple algebra, where Fq is the finite field with q=pr elements and characteristic p. It seems natural to impose to the code some extra structure such as been a subalgebra of A. In this case we will have codes that have a Mattson-Solomon transform treatment as the classical cyclic codes. Moreover, the results on the structure of semisimple finite dimensional algebras allow us to study those codes from the generator point of view.
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| first_indexed | 2025-12-07T17:45:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152365 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:45:15Z |
| publishDate | 2007 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Martınez-Moro, E. 2019-06-10T14:39:44Z 2019-06-10T14:39:44Z 2007 On semisimple algebra codes: generator theory / E. Martınez-Moro // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 3. — С. 99–112. — Бібліогр.: 21 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:13P10,94B05,94B15. https://nasplib.isofts.kiev.ua/handle/123456789/152365 The class of affine variety codes is defined as the Fq linear subspaces of A a Fq-semisimple algebra, where Fq is the finite field with q=pr elements and characteristic p. It seems natural to impose to the code some extra structure such as been a subalgebra of A. In this case we will have codes that have a Mattson-Solomon transform treatment as the classical cyclic codes. Moreover, the results on the structure of semisimple finite dimensional algebras allow us to study those codes from the generator point of view. Partially supported by Spanish MEC MTM2004-00876 and MTM2004-00958. Thisresearch was carried out while the author visited the Boole Center for Research inInformatics, University College Cork, Ireland.
 The author wants to thank Patrick Fitzpatrick and Massimiliano Sala
 for their useful discussions and hints during his visit to the Boole Center
 for Research in Informatics, University College Cork, Ireland. All the
 computations were carried out with Singular 3.0 [9]. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On semisimple algebra codes: generator theory Article published earlier |
| spellingShingle | On semisimple algebra codes: generator theory Martınez-Moro, E. |
| title | On semisimple algebra codes: generator theory |
| title_full | On semisimple algebra codes: generator theory |
| title_fullStr | On semisimple algebra codes: generator theory |
| title_full_unstemmed | On semisimple algebra codes: generator theory |
| title_short | On semisimple algebra codes: generator theory |
| title_sort | on semisimple algebra codes: generator theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152365 |
| work_keys_str_mv | AT martınezmoroe onsemisimplealgebracodesgeneratortheory |