The Hamming scheme, named after Richard Hamming, is also known as the hyper-cubic association scheme, and it is the most important example for coding theory. In this scheme the set of binary vectors of length n, and two vectors are i-th associates if they are Hamming distance i apart. Recall that an association scheme is visualized as a complete graph with labeled edges. The graph has v vertices, one for each point of X, and the edge joining vertices x and y is labeled i if x and y are i-th associates. Each edge has a unique label, and the number of triangles with a fixed base labeled k having the other edges labeled i and j is a constant c_{ijk}, depending on i,j,k but not on the choice of the base. In particular, each vertex is incident with exactly c_{ii0}=v_i edges labeled i; v_{i} is the valency of the relation R_i. The c_{ijk} in a Hamming scheme are given by Here, v=|X|=2^n and The matrices in the Bose-Mesner algebra are matrices, with rows and columns labeled by vectors In particular the (x,y)-th entry of D_{k} is 1 if and only if