Complementary properties of Hadamard matrices

This paper demonstrates and compares the complementary properties of two types of Hadamard matrices, i.e., the Walsh-Hadamard matrix and the Golay-paired Hadamard matrix. A simple process is also proposed to construct mutually orthogonal Walsh-Hadamard matrices and mutually orthogonal Golay-paired Hadamard matrices, which represent respectively a collection of mutually orthogonal complementary sets of sequences. Examples are given to verify the relationships between the two types of Hadamard matrices and illustrate the completeness and scalability of the constructed mutually orthogonal complementary sets of sequences.