In experimental situations where n three-level factors are involved and n observations are taken, we obtain orthogonal designs from weighing matrices. In factorial experiments the use of orthogonal designs contributes decisively to the reduction of variance which is considered to be a significant factor in the improvement of industrial products. Sequences with elements 0, 1, [minus ] 1 and zero autocorrelation function can be used to construct weighing matrices. In this paper we discuss some constructions of weighing designs. We give some new {0, 1, [minus ] 1} sequences with zero autocorrelation function from which we construct some new weighing matrices.