Codes in Bipartite Distance‐Regular Graphs

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 2 e ‐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 = Q k and Г = 2. O k .