Binary codes from graphs on triples Original Research Article

For a set Ω of size n⩾7 and Ω{3} the set of subsets of Ω of size 3, we examine the binary codes obtained from the adjacency matrix of each of the three graphs with vertex set Ω{3}, with adjacency defined by two vertices as 3-sets being adjacent if they have zero, one or two elements in common, respectively.