On semisimple algebra codes: generator theory
The class of affine variety codes is defined as the \(\mathbb F_q\) linear subspaces of \(\mathcal A\) a \(\mathbb F_q\)-semisimple algebra, where \(\mathbb F_q\) is the finite field with \(q=p^r\) elements and characteristic \(p\). It seems natural to impose to the code some extra structure such as...
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/861 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543221653438464 |
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| author | Martınez-Moro, Edgar |
| author_facet | Martınez-Moro, Edgar |
| author_sort | Martınez-Moro, Edgar |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T12:28:31Z |
| description | The class of affine variety codes is defined as the \(\mathbb F_q\) linear subspaces of \(\mathcal A\) a \(\mathbb F_q\)-semisimple algebra, where \(\mathbb F_q\) is the finite field with \(q=p^r\) elements and characteristic \(p\). It seems natural to impose to the code some extra structure such as been a subalgebra of \(\mathcal A\). 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. |
| first_indexed | 2025-12-02T15:41:13Z |
| format | Article |
| id | admjournalluguniveduua-article-861 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:41:13Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-8612018-03-21T12:28:31Z On semisimple algebra codes: generator theory Martınez-Moro, Edgar Semisimple Algebra, Mattson-Solomon Transform, Discrete Fourier Transform, Grobner bases 13P10,94B05,94B15 The class of affine variety codes is defined as the \(\mathbb F_q\) linear subspaces of \(\mathcal A\) a \(\mathbb F_q\)-semisimple algebra, where \(\mathbb F_q\) is the finite field with \(q=p^r\) elements and characteristic \(p\). It seems natural to impose to the code some extra structure such as been a subalgebra of \(\mathcal A\). 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. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/861 Algebra and Discrete Mathematics; Vol 6, No 3 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/861/391 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Semisimple Algebra Mattson-Solomon Transform Discrete Fourier Transform Grobner bases 13P10,94B05,94B15 Martınez-Moro, Edgar On semisimple algebra codes: generator theory |
| 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 |
| topic | Semisimple Algebra Mattson-Solomon Transform Discrete Fourier Transform Grobner bases 13P10,94B05,94B15 |
| topic_facet | Semisimple Algebra Mattson-Solomon Transform Discrete Fourier Transform Grobner bases 13P10,94B05,94B15 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/861 |
| work_keys_str_mv | AT martınezmoroedgar onsemisimplealgebracodesgeneratortheory |