On some regular Hadamard matrices and related codes

A Hadamard matrix of order m is a (m \times m) matrix H=( h_{i,j}), h_{i,j} \in \{ -1,1 \}, satisfying HH^T=H^TH=mI_m, where I_m is an (m \times m) identity matrix. A Hadamard matrix is called regular if the row and column sums are constant. It is conjectured that a regular Hadamard matrix of order 4k^2 exists for every positive integer k. We will give some method of constructing regular Hadamard matrices and related self-orthogonal codes.