Complex Hadamard Matrices and Weighing Matrices

It is shown that a weighing matrix can be obtained from any quaternary complex Hadamard matrix as well as from two suitable disjoint weighing matrices. It is also shown that Hadamard and complex Hadamard matrices can be obtained from complex weighing matrices. Weighing matrices can be regarded as ternary orthogonal code. Here rows of the matrix are taken as code words.