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Designs, Codes and Cryptography

Erschienen in:

01.07.2014

Sporadic neighbour-transitive codes in Johnson graphs

verfasst von: Max Neunhöffer, Cheryl E. Praeger

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1/2014

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Abstract

We classify the neighbour-transitive codes in Johnson graphs \(J(v,k)\) of minimum distance at least three which admit a neighbour-transitive group of automorphisms that is an almost simple two-transitive group of degree \(v\) and does not occur in an infinite family of two-transitive groups. The result of this classification is a table of 22 codes with these properties. Many have relatively large minimum distance in comparison to their length \(v\) and number of code words. We construct an additional five neighbour-transitive codes with minimum distance two admitting such a group. All 27 codes are \(t\)-designs with \(t\) at least two.

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Titel: Sporadic neighbour-transitive codes in Johnson graphs
verfasst von: Max Neunhöffer
Cheryl E. Praeger
Publikationsdatum: 01.07.2014
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1/2014
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-013-9853-0

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