Full rank perfect codes and \(\alpha \)-kernels
type: Item
instance of: scholarly article
title: Full rank perfect codes and \(\alpha \)-kernels
zbMATH Open document ID: 1171.94010
author: Olof Heden
published in: Discrete Mathematics
publication date: 2009-06-19T00:00:00Z
review text: There are few general constructions of full rank perfect codes, that are not given by recursive methods using perfect codes of length shorter than \(n= 2^m-1\). In this paper, the author constructs full rank perfect codes, the so-called normal \(\alpha\)-codes, by first finding the superdual of the perfect code. The kernel of such normal \(\alpha\)-codes have also been considered and it is proved that any subspace of the kernel of a normal \(\alpha\)-code that satisfies a certain property is the kernel of another perfect code of the same length \(n\). In this way, the author has been able to relate some of the full rank perfect codes of length \(n\) to other full rank perfect codes of the same length \(n\).
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 94B60
zbMATH DE Number: 5566687
zbMATH Keywords: perfect codes
zbMATH Keywords: full rank perfect codes
zbMATH Keywords: normal \(\alpha\)-codes
zbMATH Keywords: simplex codes
zbMATH Keywords: superdual of perfect code
MaRDI profile type: Publication
full work available at URL: j.disc.2008.04.051
OpenAlex ID: W2016928832
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DOI: 10.1016/J.DISC.2008.04.051
description: scientific article; zbMATH DE number 5566687