Ternary codes from graphs on triples

For a set ΩΩ of size n≥7n≥7 and Ω{3}Ω{3} the set of subsets of ΩΩ of size 33, we examine the ternary codes obtained from the adjacency matrix of each of the three graphs with vertex set Ω{3}Ω{3}, with adjacency defined by two vertices as 33-sets being adjacent if they have zero, one or two elements in common, respectively.