Codes from the incidence matrices of graphs on 3-sets

We examine the pp-ary linear codes from incidence matrices of the three uniform subset graphs with vertex set the set of subsets of size 3 of a set of size nn, with adjacency defined by two vertices as 3-sets being adjacent if they have zero, one or two elements in common, respectively. All the main parameters of the codes and the nature of the minimum words are obtained, and it is shown that the codes can be used for full error-correction by permutation decoding. We examine also the binary codes of the line graphs of these graphs.