Bitwise Operations Related to a Combinatorial Problem on Binary Matrices

Some techniques for the use of bitwise operations are described in the article. As an example, an open problem of isomorphism-free generations of combinatorial objects is discussed. An equivalence relation on the set of square binary matrices having the same number of units in each row and each column is defined. Each binary matrix is represented using ordered n-tuples of natural numbers. It is shown how by using the bitwise operations can be implemented an algorithm that gets canonical representatives which are extremal elements of equivalence classes relative to a double order on the set of considered objects.