A remark on the intersection arrays of distance-regular graphs

AbstractIt is shown that the number of columns of type (1, 1, k − 2) in the intersection array of a distance-regular graph with valency k and girth >3 is at most four

Families of nested completely regular codes and distance-regular graphs

In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius $\rho$ equal to $3$ or $4$, and are $1/2^i$-th parts, for $i\in\{1,\ldots,u\}$ of binary (respectively, extended binary) Hamming codes of length $n=2^m-1$ (respectively, $2^m$), where $m=2u$. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter $D$ equal to $3$ or $4$ are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive