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}
}
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… 
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References

SHOWING 1-10 OF 35 REFERENCES
Neighbour-transitive codes in Johnson graphs
TLDR
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.
On Sets with Few Intersection Numbers in Finite Projective and Affine Spaces
In this paper we study sets $X$ of points of both affine and projective spaces over the Galois field $\mathop{\rm{GF}}(q)$ such that every line of the geometry that is neither contained in $X$ nor
Completely Regular Designs of Strength One
We study a class of highly regular t-designs. These are the subsets of vertices of the Johnson graph which are completely regular in the sense of Delsarte [2]. In [9], Meyerowitz classified the
Completely regular designs
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.
A Design and a Code Invariant under the Simple Group Co3
Permutation Groups
Whatever you have to do with a structure-endowed entity Σ try to determine its group of automorphisms. .. You can expect to gain a deep insight into the constitution of Σ in this way. 1 Automorphism
Bounds for binary codes of length less than 25
Improved bounds for A(n,d) , the maximum number of codewords in a (linear or nonlinear) binary code of word length n and minimum distance d , and for A(n,d,w) , the maximum number of binary vectors
Design Theory
TLDR
An overview of the ongoing discussion on ISDTs is given and fundamental concepts of ISDT are introduced, and an overview on seminal contributions to the field of IS DTs in chronological order is given.
and R
  • A. Wilson, Atlas of finite groups, Oxford University Press, Eynsham,
  • 1985
and C
  • E. Praeger, Neighbour-transitive codes in Johnson graphs, preprint,
  • 2012
...
...