Minimal binary 2-neighbour-transitive codes

Daniel R. Hawtin; Cheryl E. Praeger

doi:10.1016/j.jcta.2019.105173

Minimal binary 2-neighbour-transitive codes

Daniel R. Hawtin, Cheryl E. Praeger

Mathematics and Statistics

Research output: Contribution to journal › Article

Abstract

The main result here is a characterisation of binary 2-neighbour-transitive codes with minimum distance at least 5 via their minimal subcodes, which are found to be generated by certain designs. The motivation for studying this class of codes comes primarily from their relationship to the class of completely regular codes. The results contained here yield many more examples of 2-neighbour-transitive codes than previous classification results of families of 2-neighbour-transitive codes. In the process, new lower bounds on the minimum distance of particular sub-families are produced. Several results on the structure of 2-neighbour-transitive codes with arbitrary alphabet size are also proved. The proofs of the main results apply the classification of minimal and pre-minimal submodules of the permutation modules over F₂ for finite 2-transitive permutation groups.

Original language	English
Pages (from-to)	105-173
Journal	Journal of Combinatorial Theory. Series A
Volume	171
DOIs	https://doi.org/10.1016/j.jcta.2019.105173
Publication status	Published - 1 Apr 2020

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10.1016/j.jcta.2019.105173

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Projects

1 Finished

Group Actions: Combinatorics, Geometry and Computation

Praeger, C.

ARC Federation Fellowships

1/01/07 → 31/12/12

Project: Research

Cite this

Hawtin, D. R., & Praeger, C. E. (2020). Minimal binary 2-neighbour-transitive codes. Journal of Combinatorial Theory. Series A, 171, 105-173. https://doi.org/10.1016/j.jcta.2019.105173

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