Put d=min(m,D0) and choose the least power of two q with qd>=m. Then m<=qd<2m. Take two copies of binary strings of length log2 q as left and right vertices. For each left vertex u and port j=1,...,d add the edge (u,j) to right vertex u XOR s_j, using a selected shift s_j. XOR means coordinatewise addition modulo two. Every vertex has exactly d incident edges. Parallel edges remain DISTINCT coordinates indexed by (u,j), even when two shifts coincide. The eventual code uses edge bits, not vertex bits; this distinction matters when counting length and checking local constraints.