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 |
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| 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| Summary: | 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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| ISSN: | 1726-3255 |