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Sporadic neighbour-transitive codes in Johnson graphs

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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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Acknowledgments

Cheryl E. Praeger was supported by Australian Research Council Federation Fellowship FF0776186.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Mathematical Institute, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, UK

    Max Neunhöffer

  2. School of Mathematics and Statistics (M019), The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Cheryl E. Praeger

  3. King Abdulaziz University, Jidda, Saudi Arabia

    Cheryl E. Praeger

Authors
  1. Max Neunhöffer
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  2. Cheryl E. Praeger
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Correspondence to Cheryl E. Praeger.

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This is one of several papers published in Designs, Codes and Cryptography comprising the special topic on “Finite Geometries: A special issue in honor of Frank De Clerck”.

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Neunhöffer, M., Praeger, C.E. Sporadic neighbour-transitive codes in Johnson graphs. Des. Codes Cryptogr. 72, 141–152 (2014). https://doi.org/10.1007/s10623-013-9853-0

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