Abstract

A new method of generating Williamson type Matrices A, B, C, D is described such that (i) A, B, C, D are symmetric. (ii) A, B, C are circulant matrices and D is a back circulant matrix. All such Williamsom type matrices of order n = 7, 9, 11, 13, 15, 17 are obtained by exhaustive computer search. The number of Williamson type Matrices constructed here is much greater than that of Williamson Matrices of same order. For example there are only 4 Williamson Matrices of order 17 but by our method we have obtained 504 Williamson type Matrices of order 17.