Hadamard matrices and submatrices

Shrinkande and Bhagwan Das (1970) showed how to extend a (4 t – 1, 4 t ) row-orthogonal matrix with entries ± 1 to a Hadamard matrix of order 4 t . Using a slightly different approach we consider extensions of (4 t – k , 4 t ) row-orthogonal matrix to a Hadamard matrix of order 4 t .