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arXiv · 2407.09803

Group actions on codes in graphs

Daniel R. Hawtin·Cheryl E. Praeger
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Abstract

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.

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Daniel R. Hawtin, Cheryl E. Praeger. 2024-07-13. Group actions on codes in graphs. https://arxiv.org/abs/2407.09803

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