Tri-weight Codes and Generalized Hadamard Matrices

The existence is shown of a set of (p~ -1) generalized Hadamard matrices H(p, p~'~) of order p2'~, each of which is symmetric and regular. When normalized to become unitary matrices, they form a multiplicative group of order p'~, simply isomorphic to the additive group of GF(pm). The rows of these (p~ 1) matrices are shown to be the image, under the well-known isomorphic mapping relating the pth roots of unity to the elements of GF(p), of the set of vectors of a given weight in the tri-weight extended-BCIt code of length p2~% dimension 3m ~ 1, and minimum weight (p 1)p 2'~-1 pro-1.