Honold, Thomas; Landjev, Ivan Linear codes over finite chain rings. (English) Zbl 1025.94017 Electron. J. Comb. 7, No. 1, Research paper R11, 22 p. (2000); printed version J. Comb. 7, No. 1 (2000). Summary: 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. Cited in 41 Documents MSC: 94B05 Linear codes (general theory) 51C05 Ring geometry (Hjelmslev, Barbilian, etc.) 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) Keywords:linear codes; finite chain rings; geometric viewpoint; projective Hjelmslev geometries; MacDonald codes PDFBibTeX XMLCite \textit{T. Honold} and \textit{I. Landjev}, Electron. J. Comb. 7, No. 1, Research paper R11, 22 p. (2000); printed version J. Comb. 7, No.1 (2000; Zbl 1025.94017) Full Text: EuDML EMIS