Group actions on codes in graphs
<|reference_start|>Group actions on codes in graphs: This is a chapter in a forthcoming book on completely regular codes in distance regular graphs. The chapter provides an overview, and some original results, on codes in distance regular graphs which admit symmetries via a permutation group acting on the vertices of the graph. The strongest notion of completely transitive codes is developed, as well as the more general notion of neighbour-transitive codes. The graphs considered are the Hamming, Johnson, and Kneser graphs and their q-analogues, as well as some graphs related to incidence structures.<|reference_end|>
@article{hawtin2024group,
    title={Group actions on codes in graphs},
    author={Daniel R. Hawtin and Cheryl E. Praeger},
    journal={arXiv preprint arXiv:2407.09803},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.09803},
    primaryClass={math.CO cs.IT math.IT}
}