# Sporadic neighbour-transitive codes in Johnson graphs

@article{Neunhffer2014SporadicNC,
title={Sporadic neighbour-transitive codes in Johnson graphs},
author={Max Neunh{\"o}ffer and Cheryl E. Praeger},
journal={Designs, Codes and Cryptography},
year={2014},
volume={72},
pages={141-152}
}
• Published 2 August 2013
• Mathematics
• Designs, Codes and Cryptography
We classify the neighbour-transitive codes in Johnson graphs $$J(v,k)$$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 $$v$$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 $$v$$v and number of code words. We…
9 Citations
Neighbour-transitive codes in Johnson graphs
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It is proved that, provided distinct codewords are at distance at least $$3$$3, then G is 2-transitive on V, which is many of the infinite families of finite $$2$$2- transitive permutation groups and construct surprisingly rich families of examples of neighbour-transitives codes.
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We study a class of t-designs which enjoy a high degree of regularity. These are the subsets of vertices of the Johnson graph which are completely regular, in the sense of Delsarte [Philips Res.
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