Anticodes for the Grassman and bilinear forms graphs

In [2], L. Chihara proved that many infinite families of classical distance-regular graphs have no nontrivial perfect codes, including the Grassman graphs and the bilinear forms graphs. Here, we present a new proof of her result for these two families using Delsarte's anticode condition[3]. The technique is an extension of an approach taken by C. Roos [6] in the study of perfect codes in the Johnson graphs.