CONSTRUCTIONS FOR THE SPARSEST ORTHOGONAL MATRICES

In [1], it was shown that for the least number of nonzero entries in an orthogonal matrix is not direct summable is 4n-4, and zero patterns of the orthogonal matrices with exactly 4n-4 nonzero entries were determined. In this paper, we construct orthogonal matrices with exactly 4n-r nonzero entries. furthermore, we determine mn sparse row-orthogonal matrices.