Codes from incidence matrices and line graphs of Hamming graphs

We examine the p -ary codes, for any prime p , that can be obtained from incidence matrices and line graphs of the Hamming graphs, H ( n , m ) , obtaining the main parameters of these codes. We show that the codes from the incidence matrices of H ( n , m ) can be used for full permutation decoding for all m , n ≥ 3 .