It is shown that if there exists a binary code C of length d and covering radius k then a zonotope in the d-dimensional Euclidean space can be illuminated by C affine subspaces of dimension k. Applying results from coding theory, the exact value of the illumination numbers of d-dimensional parallelotopes is determined in some special cases.
A new preconditioned conjugate gradient (PCG)-based domain decomposition method is given for the solution of linear equations
arising in the finite element method applied to the elliptic Neumann problem. The novelty of the proposed method is in the
recommended preconditioner which is constructed by using cyclic matrix. The resulting preconditioned algorithms are well suited
to parallel computation.