Seek a matrix M and measurement matrix C. First, M must fix the kernel of C, so (I-M)zeta is known from measurements. Second, each nonzero coefficient M[u,y] must have at most R-1 mismatched points E_{u,y}={t:a_y(t)!=d_u(t)}. Use the identity zeta_u=((I-M)zeta)_u+sum_y M[u,y]zeta_y. Leave the first term unchanged and multiply each term of the sum by the zero-making polynomial for its mismatched points. At zero the identity is restored. At point t, every surviving term uses a coordinate in the assigned group. The degree is at most R-1. The remaining task is to construct M and C with these two properties and few measurement rows.