Geodesic
On the lattice of cyclic codes over finite chain rings
Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 252-268.

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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.
Keywords: finite chain rings, cyclotomic cosets, linear code, trace map.
Mots-clés : cyclic code 
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Alexandre Fotue-Tabue; Christophe Mouaha. On the lattice of cyclic codes over finite chain rings. Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 252-268. http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a7/

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