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 
@article{ADM_2019_27_2_a7,
     author = {Alexandre Fotue-Tabue and Christophe Mouaha},
     title = {On the lattice of cyclic codes over finite chain rings},
     journal = {Algebra and discrete mathematics},
     pages = {252--268},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a7/}
}
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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/