Binary Codes and Partial Permutation Decoding Sets from the Johnson Graphs

摘要

For , , the Johnson graph denoted by is the graph with vertex-set the set of all -subsets of , and any two vertices and are adjacent if and only if . In this paper the binary codes and their duals generated by an adjacency matrix of are described. The automorphism groups of the codes are determined, and by identifying suitable information sets, 3-PD-sets are determined for the code when is even.