A Novel Family of Complex Hadamard Matrices with Cyclically Distinct Rows and Large Linear Span

Hadamard matrices are widely applied to communications. A novel family of complex Hadamard matrices, whose rows are cyclically distinct and have large linear span, is presented. As a consequence,the security of the system employing the proposed complex Hadamard matrices is greatly improved, which means that these new complex Hadamard matrices are good candidates in engineering applications.In addition, the proposed method in this paper can also produce binary Hadamard matrices, which is carried out by setting simply the parameter p = 2.