Geodesic
Linear codes over finite chain rings
The electronic journal of combinatorics, Tome 7 (2000)
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The aim of this paper is to develop a theory of linear codes over finite chain rings from a geometric viewpoint. Generalizing a well-known result for linear codes over fields, we prove that there exists a one-to-one correspondence between so-called fat linear codes over chain rings and multisets of points in projective Hjelmslev geometries, in the sense that semilinearly isomorphic codes correspond to equivalent multisets and vice versa. Using a selected class of multisets we show that certain MacDonald codes are linearly representable over nontrivial chain rings.
DOI : 10.37236/1489
Classification : 94B05, 51C05, 11T71
Mots-clés : linear codes, finite chain rings, geometric viewpoint, projective Hjelmslev geometries, MacDonald codes 
@article{10_37236_1489,
     author = {Thomas Honold and Ivan Landjev},
     title = {Linear codes over finite chain rings},
     journal = {The electronic journal of combinatorics},
     year = {2000},
     volume = {7},
     doi = {10.37236/1489},
     zbl = {1025.94017},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1489/}
}
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Thomas Honold; Ivan Landjev. Linear codes over finite chain rings. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1489

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