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
Main Author: Martınez-Moro, E.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2007
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
id nasplib_isofts_kiev_ua-123456789-152365
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title On semisimple algebra codes: generator theory
spellingShingle On semisimple algebra codes: generator theory
Martınez-Moro, E.
title_short 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_sort on semisimple algebra codes: generator theory
author Martınez-Moro, E.
author_facet Martınez-Moro, E.
publishDate 2007
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
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.
issn 1726-3255
url https://nasplib.isofts.kiev.ua/handle/123456789/152365
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.
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last_indexed 2025-12-07T17:45:15Z
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