Group actions on codes in graphs
Combinatorics
2024-07-16 v1 Information Theory
math.IT
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.
Cite
@article{arxiv.2407.09803,
title = {Group actions on codes in graphs},
author = {Daniel R. Hawtin and Cheryl E. Praeger},
journal= {arXiv preprint arXiv:2407.09803},
year = {2024}
}
Comments
50 pages