Matrices for graphs designs and codes

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

Abstract

The adjacency matrix of a graph can be interpreted as the incidence matrix of a design, or as the generator matrix of a binary code. Here these relations play a central role. We consider graphs for which the corresponding design is a (symmetric) block design or (group) divisible design. Such graphs are strongly regular (in case of a block design) or very similar to a strongly regular graph (in case of a divisible design). Many constructions and properties for these kind of graphs are obtained. We also consider the binary code of a strongly regular graph, work out some theory and give several examples.
Original languageEnglish
Title of host publicationInformation Security, Coding Theory and Related Combinatorics
Subtitle of host publicationInformation coding and combinatories
EditorsD. Crnkovic, V. Tonchev
Place of PublicationAmsterdam
PublisherIOS Press
Pages253-277
Number of pages460
ISBN (Print)9781607506638
Publication statusPublished - 2011

Publication series

NameNATO Science for Peace and Security Series - D: Information and Communication Security
Number29

Fingerprint

Graph Design
Strongly Regular Graph
Block Design
Binary Code
Graph in graph theory
Group Divisible Design
Symmetric Design
Incidence Matrix
Adjacency Matrix
Divisible
Generator
Design

Cite this

Haemers, W. H. (2011). Matrices for graphs designs and codes. In D. Crnkovic, & V. Tonchev (Eds.), Information Security, Coding Theory and Related Combinatorics: Information coding and combinatories (pp. 253-277). (NATO Science for Peace and Security Series - D: Information and Communication Security; No. 29). Amsterdam: IOS Press.
Haemers, W.H. / Matrices for graphs designs and codes. Information Security, Coding Theory and Related Combinatorics: Information coding and combinatories. editor / D. Crnkovic ; V. Tonchev. Amsterdam : IOS Press, 2011. pp. 253-277 (NATO Science for Peace and Security Series - D: Information and Communication Security; 29).
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Haemers, WH 2011, Matrices for graphs designs and codes. in D Crnkovic & V Tonchev (eds), Information Security, Coding Theory and Related Combinatorics: Information coding and combinatories. NATO Science for Peace and Security Series - D: Information and Communication Security, no. 29, IOS Press, Amsterdam, pp. 253-277.

Matrices for graphs designs and codes. / Haemers, W.H.

Information Security, Coding Theory and Related Combinatorics: Information coding and combinatories. ed. / D. Crnkovic; V. Tonchev. Amsterdam : IOS Press, 2011. p. 253-277 (NATO Science for Peace and Security Series - D: Information and Communication Security; No. 29).

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

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AB - The adjacency matrix of a graph can be interpreted as the incidence matrix of a design, or as the generator matrix of a binary code. Here these relations play a central role. We consider graphs for which the corresponding design is a (symmetric) block design or (group) divisible design. Such graphs are strongly regular (in case of a block design) or very similar to a strongly regular graph (in case of a divisible design). Many constructions and properties for these kind of graphs are obtained. We also consider the binary code of a strongly regular graph, work out some theory and give several examples.

M3 - Chapter

SN - 9781607506638

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BT - Information Security, Coding Theory and Related Combinatorics

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Haemers WH. Matrices for graphs designs and codes. In Crnkovic D, Tonchev V, editors, Information Security, Coding Theory and Related Combinatorics: Information coding and combinatories. Amsterdam: IOS Press. 2011. p. 253-277. (NATO Science for Peace and Security Series - D: Information and Communication Security; 29).