A combinatorial construction of the Gray map over Galois rings
type: Item
instance of: scholarly article
title: A combinatorial construction of the Gray map over Galois rings
zbMATH Open document ID: 1183.94061
author: Bahattin Yildiz
published in: Discrete Mathematics
publication date: 2009-06-23T00:00:00Z
review text: A Gray map is defined to be a weight preserving map from \(\mathbb{R}^n\) with the homogeneous weight to \(F^m\) with the Hamming weight where \(R\) is a ring and \(F\) is a field. Gray maps are an extremely important object of study in coding theory and are one of the reasons why codes over rings have become increasingly studied. The author gives an interesting new combinatorial construction of Gray maps when \(R\) is a Galois ring using affine hyperplanes in an associated affine geometry.
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 94B27
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 5569089
zbMATH Keywords: linear codes
zbMATH Keywords: Galois rings
zbMATH Keywords: homogeneous weights
zbMATH Keywords: Gray maps
zbMATH Keywords: affine geometries
zbMATH Keywords: affine hyperplanes
MaRDI profile type: Publication
full work available at URL: j.disc.2008.09.002
OpenAlex ID: W2048771505
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DOI: 10.1016/J.DISC.2008.09.002
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description: scientific article; zbMATH DE number 5569089