Codes and anticodes in the Grassman graph
type: Item
instance of: scholarly article
title: Codes and anticodes in the Grassman graph
zbMATH Open document ID: 1006.94028
author: Moshe Schwartz
author: Tuvi Etzion
published in: Journal of Combinatorial Theory. Series A
publication date: 2002-07-04T00:00:00Z
review text: The authors examine perfect codes and optimal anticodes in the Grassman graph \(G_q(n, k)\). It is shown that the vertices of the Grassman graph cannot be partitioned into optimal anticodes, with a possible exception when \(n= 2k\). Properties of diameter perfect codes in the graph are also examined. These codes are known to be similar to Steiner systems. Connections between these systems and ``real'' Steiner systems are discussed.
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 05D05
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 1763792
zbMATH Keywords: perfect codes
zbMATH Keywords: optimal anticodes
zbMATH Keywords: Grassman graph
zbMATH Keywords: Steiner systems
MaRDI profile type: Publication
full work available at URL: jcta.2001.3188
OpenAlex ID: W1996897280
cites work: On perfect codes and related concepts
cites work: Q5707657
cites work: On the Nonexistence of Perfect Codes in the Johnson Scheme
cites work: Perfect byte-correcting codes
cites work: The Erdős-Ko-Rado theorem for vector spaces
cites work: Anticodes for the Grassmann and bilinear forms graphs
DOI: 10.1006/JCTA.2001.3188
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description: scientific article; zbMATH DE number 1763792