Journal of the
Korean Mathematical Society JKMS

In [4], it was shown that an $n$ by $n$ orthogonal matrix which has a row of nonzeros has at least $$ (\lfloor\text{log}_2n\rfloor+3)n-2^{\lfloor\text{log}_2n\rfloor+1} $$ nonzero entries. In this paper, the matrices achieving these bounds are constructed. The analogous sparsity problem for $m$ by $n$ row-orthogonal matrices which have a row of nonzeros is conjectured.

Keywords: sparse orthogonal matrix, row-orthogonal matrix

MSC numbers: Primary 05A15; Secondary 65F25