Codes from the incidence matrices and line graphs of Hamming graphs $H^k(n,2)$ for $k \geq 2$

Abstract

We examine the $p$-ary codes, for any prime $p$, that can be obtained from incidence matrices and line graphs of the Hamming graphs, $H^k(n,m)$, for $k \geq 2$. For $m=2$, we obtain the main parameters of the codes from the incidence matrices, including the minimum weight and the nature of the minimum words. We show that all the codes can be used for full permutation decoding.