2024/07/13 by Hawtin, Daniel R., Praeger, Cheryl E.
#05E18 (Primary) 94B99 (Secondary) #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2407.09803
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.