Linear codes over finite chain rings
type: Item
instance of: scholarly article
title: Linear codes over finite chain rings
zbMATH Open document ID: 1025.94017
author: Thomas Honold
author: I. Landjev
published in: The Electronic Journal of Combinatorics
publication date: 2000-03-12T00:00:00Z
full work available at URL: https://eudml.org/doc/123043
full work available at URL: v7i1r11.html
review text: 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.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 51C05
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 1413179
zbMATH Keywords: linear codes
zbMATH Keywords: finite chain rings
zbMATH Keywords: geometric viewpoint
zbMATH Keywords: projective Hjelmslev geometries
zbMATH Keywords: MacDonald codes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1413179