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...
Gespeichert in:
| Datum: | 2019 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2019
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/431 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543205373247488 |
|---|---|
| author | Fotue-Tabue, Alexandre Mouaha, Christophe |
| author_facet | Fotue-Tabue, Alexandre Mouaha, Christophe |
| author_sort | Fotue-Tabue, Alexandre |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2019-07-14T19:54:06Z |
| 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. |
| first_indexed | 2026-02-08T07:56:50Z |
| format | Article |
| id | admjournalluguniveduua-article-431 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:56:50Z |
| publishDate | 2019 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| title | 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_short | On the lattice of cyclic codes over finite chain rings |
| title_sort | on the lattice of cyclic codes over finite chain rings |
| topic | finite chain rings cyclotomic cosets linear code cyclic code trace map 13B05 94B05 94B15 03G10 16P10 |
| topic_facet | finite chain rings cyclotomic cosets linear code cyclic code trace map 13B05 94B05 94B15 03G10 16P10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/431 |
| work_keys_str_mv | AT fotuetabuealexandre onthelatticeofcycliccodesoverfinitechainrings AT mouahachristophe onthelatticeofcycliccodesoverfinitechainrings |