Codes in Bipartite Distance-Regular Graphs
Eiichi Bannaĭ · Journal of the London Mathematical Society · 1977
For each bipartition of a bipartite distance-regular graph Г, there naturally corresponds another distance-regular graph Γ ¯ called a halved graph. It is shown that the existence of a perfect e-code in a halved graph Γ ¯ is equivalent to the existence of a uniformly packed 2e-code in Г with certain specific parameters. Using this equivalence, we show the non-existence of perfect codes for two classes of distance-regular graphs Γ ¯ corresponding to Г = Qk and Г = 2. Ok.