Codes from graphs related to the categorical product of triangular graphs and Kn

For any prime p and n ≥ 3, we examine p-ary linear codes generated by incidence matrices of two classes of graphs, H_n and Γ_n where H_n-1 is an induced subgraph of Γ_n. Γ_n is a subgraph of the union of the categorical product of triangular graphs T_n and complete graphs K_n, and complements of triangular graphs T̅_n and K_n, where the union of graphs is as defined in. For the codes of H_n, we exhibit permutation decoding sets of order n for full error correction. Their size is only twice the lower bound due to Gordon. We also consider partial permutation decoding for the binary codes from Γ_n.