Matrices of zeros and ones with given line sums and a zero block

Motivated by certain reconstruction problems in discrete tomography we study the existence of (0, 1)-matrices with given line sums and a fixed zero block. An algorithm is given to construct such a matrix which is based on three applications of the well-known Gale-Ryser algorithm for constructing (0, 1)-matrices with given line sums. A characterization in terms of a certain “structure matrix” is proved. We also briefly discuss some generalizations where zeros may be fixed in other positions.