On the lattice of cyclic codes over finite chain rings

• Date: 2019
• Main Authors: Fotue-Tabue, Alexandre, Mouaha, Christophe
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2019
• Subjects: finite chain rings; cyclotomic cosets; linear code; cyclic code; trace map; 13B05; 94B05; 94B15; 03G10; 16P10
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/431
• Journal Title: Algebra and Discrete Mathematics

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...