On the lattice of cyclic codes over finite chain rings
In this paper, \(R\) is a finite chain ring of invariants \((q,s)\), and \(\ell\) is a positive integer fulfilling \(\operatorname{gcd}(\ell,q) = 1\). In the language of \(q\)-cyclotomic cosets modulo \(\ell\), the cyclic codes over \(R\) of length \(\ell\) are uniquely decomposed into a direct sum...
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| Datum: | 2019 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2019
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-4312019-07-14T19:54:06Z On the lattice of cyclic codes over finite chain rings Fotue-Tabue, Alexandre Mouaha, Christophe finite chain rings, cyclotomic cosets, linear code, cyclic code, trace map 13B05, 94B05, 94B15, 03G10, 16P10 In this paper, \(R\) is a finite chain ring of invariants \((q,s)\), and \(\ell\) is a positive integer fulfilling \(\operatorname{gcd}(\ell,q) = 1\). In the language of \(q\)-cyclotomic cosets modulo \(\ell\), the cyclic codes over \(R\) of length \(\ell\) are uniquely decomposed into a direct sum of trace-representable cyclic codes over \(R\) and the lattice of cyclic codes over \(R\) of length \(\ell\) is investigated. Lugansk National Taras Shevchenko University 2019-07-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/431 Algebra and Discrete Mathematics; Vol 27, No 2 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/431/pdf Copyright (c) 2019 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2019-07-14T19:54:06Z |
| collection |
OJS |
| language |
English |
| topic |
finite chain rings cyclotomic cosets linear code cyclic code trace map 13B05 94B05 94B15 03G10 16P10 |
| spellingShingle |
finite chain rings cyclotomic cosets linear code cyclic code trace map 13B05 94B05 94B15 03G10 16P10 Fotue-Tabue, Alexandre Mouaha, Christophe On the lattice of cyclic codes over finite chain rings |
| topic_facet |
finite chain rings cyclotomic cosets linear code cyclic code trace map 13B05 94B05 94B15 03G10 16P10 |
| format |
Article |
| author |
Fotue-Tabue, Alexandre Mouaha, Christophe |
| author_facet |
Fotue-Tabue, Alexandre Mouaha, Christophe |
| author_sort |
Fotue-Tabue, Alexandre |
| title |
On the lattice of cyclic codes over finite chain rings |
| title_short |
On the lattice of cyclic codes over finite chain rings |
| title_full |
On the lattice of cyclic codes over finite chain rings |
| title_fullStr |
On the lattice of cyclic codes over finite chain rings |
| title_full_unstemmed |
On the lattice of cyclic codes over finite chain rings |
| title_sort |
on the lattice of cyclic codes over finite chain rings |
| description |
In this paper, \(R\) is a finite chain ring of invariants \((q,s)\), and \(\ell\) is a positive integer fulfilling \(\operatorname{gcd}(\ell,q) = 1\). In the language of \(q\)-cyclotomic cosets modulo \(\ell\), the cyclic codes over \(R\) of length \(\ell\) are uniquely decomposed into a direct sum of trace-representable cyclic codes over \(R\) and the lattice of cyclic codes over \(R\) of length \(\ell\) is investigated. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2019 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/431 |
| work_keys_str_mv |
AT fotuetabuealexandre onthelatticeofcycliccodesoverfinitechainrings AT mouahachristophe onthelatticeofcycliccodesoverfinitechainrings |
| first_indexed |
2025-07-17T10:34:29Z |
| last_indexed |
2025-07-17T10:34:29Z |
| _version_ |
1837889979510947840 |