W. Fish

Oct 15, 2014

Citations

0

Influential Citations

8

Citations

Journal

Graphs and Combinatorics

Abstract

For $$k \ge 1$$k≥1, $$n \ge 2k$$n≥2k, the Johnson graph denoted by $$J(n,k),$$J(n,k), is the graph with vertex-set the set of all $$k$$k-subsets of $$\Omega = \{1, 2, \ldots , n\}$$Ω={1,2,…,n}, and any two vertices $$u$$u and $$v$$v are adjacent if and only if $$|u \cap v| = k-1$$|u∩v|=k-1. In this paper the binary codes and their duals generated by an adjacency matrix of $$J(n,k)$$J(n,k) 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 $$k$$k is even.