Completely transitive codes in Hamming graphs
type: Item
instance of: scholarly article
title: Completely transitive codes in Hamming graphs
zbMATH Open document ID: 0943.05042
author: Michael Giudici
author: Cheryl E. Praeger
published in: European Journal of Combinatorics
publication date: 2000-03-02T00:00:00Z
review text: A code \(C\) in the graph \(\Gamma\) is a non-empty subset of the vertex set \(V\) of \(\Gamma\). Completely transitive codes are a special class of completely regular codes. A code in the graph \(\Gamma\) is called a completely transitive code if there exists a subgroup \(G\) of the group of automorphisms of \(\Gamma\), such that each cell \(C_i\) in the distance partition of \(C\) is an orbit of \(G\). The authors consider completely transitive codes in Hamming graphs. The vertices of the Hamming graph \(H(m,q)\) are the \(m\)-tuples with entries from a set \(Q\) of size \(q\). Two vertices are joined by an edge iff they differ in exactly one entry. The authors prove a structure theorem which shows that completely transitive codes are made up of either transitive or nearly complete, completely transitive codes.
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1382657
zbMATH Keywords: transitive codes
zbMATH Keywords: group of automorphisms
zbMATH Keywords: Hamming graphs
Wikidata QID: Q56988039
reviewed by: Ulrike Baumann
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: eujc.1999.0313
OpenAlex ID: W2009956376
cites work: Q3050438
cites work: Q3992965
cites work: Problems in algebraic combinatorics
cites work: Q4146667
cites work: Completely regular codes
cites work: Completely regular codes and completely transitive codes
DBLP publication ID: journals/ejc/GiudiciP99
DOI: 10.1006/EUJC.1999.0313
description: scientific article; zbMATH DE number 1382657