On an Algorithm for Obtaining All Binary Matrices of Special Class Related to V. E. Tarakanov's Formula

Abstract: An algorithm for obtaining all n\times n binary matrices having exactly 2 units in every row and every column is described in the paper. After analysing the work of the algorithm a formula for calculating the number of these matrices has been obtained. This formula is known and has been obtained using other methods, which by their nature are purely analytical and not constructive. Thus a new, constructive proof of this known formula has been obtained.