Minimal PD-sets for codes associated with the graphs Qm2, m even

Please read abstract in the article.The National Research Foundation of South Africahttp://link.springer.com/journal/2002021-12-08hj2021Mathematics and Applied Mathematic

Binary codes from m-ary n-cubes Q(n) (m)

We examine the binary codes from adjacency matrices of the graph with vertices the nodes of the m-ary n-cube Qmn and with adjacency de ned by the Lee metric. For n = 2 and m odd, we obtain the parameters of the code and its dual, and show the codes to be LCD. We also nd s-PD-sets of size s + 1 for s < m1 2 for the dual codes, i.e. [m2; 2m 1;m]2 codes, when n = 2 and m 5 is odd