The poset structures admitting the extended binary Hamming code to be a perfect code
type: Item
instance of: scholarly article
title: The poset structures admitting the extended binary Hamming code to be a perfect code
zbMATH Open document ID: 1077.94022
author: Jong Yoon Hyun
author: Hyun Kwang Kim
published in: Discrete Mathematics
publication date: 2005-01-13T00:00:00Z
review text: The authors characterize the partially ordered sets (posets) \(P\) for which an extended binary Hamming code is a double or triple error-correcting perfect code under the poset metric \(d_{P}\). For the two extended Hamming codes such posets are showed explicitly. These results follow and complete a previous work by \textit{R.A. Brualdi}, \textit{J.S. Graves} and \textit{K.M. Lawrence} in [Discrete Math. 147, 57--72 (1995; Zbl 0854.94019)].
reviewed by: Carlos Munuera
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 94B65
zbMATH DE Number: 2127153
zbMATH Keywords: poset codes
zbMATH Keywords: perfect codes
zbMATH Keywords: extended Hamming codes
MaRDI profile type: Publication
full work available at URL: j.disc.2004.07.010
OpenAlex ID: W2067929867
cites work: Classification of perfect linear codes with crown poset structure
cites work: Codes with a poset metric
cites work: Q4146667
cites work: Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes
DOI: 10.1016/J.DISC.2004.07.010
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description: scientific article; zbMATH DE number 2127153