Let V = mk + 1 be a prime power; we show for m even it is not possible to partition the Galois field GF(v) to give four (0, 1, −1) matrices X1, X2, X3, X4 satisfying:
(i) Xi * Xj = 0, i ≠ j, i, j = 1, 2, 3, 4;
(ii) is a (1, −1) matrix;
(iii) Thus this method of partitioning the Galois field GF(V), into four matrices satisfying the above conditions, cannot be used to find Baumert-Hall Hadamard arrays BH[4V] for v = 9, 11, 17, 23, 27, 29, ….