Distance-regular subgraphs in a distance-regular graph, I

Let Γ be a distance-regular graph with r = l(1, 0, k − 1) > 0 and c2r+1 = 1. We show the existence of a Moore graph of diameter r + 1 and valency ar+1 + 1 as a subgraph in Γ. In particular, we show that either ar+1 = 1 or r = 1.