Binary codes from graphs on triples

For a set <f>Ω</f> of size <f>n&ges;7</f> and <f>Ω{3}</f> the set of subsets of <f>Ω</f> of size <f>3</f>, we examine the binary codes obtained from the adjacency matrix of each of the three graphs with vertex set <f>Ω{3}</f>, with adjacency defined by two vertices as <f>3</f>-sets being adjacent if they have zero, one or two elements in common, respectively. [Copyright &y& Elsevier]