Hadamard matrices are useful in Hadamard transform spectroscopy and in the construction of optimal chemical designs.'-8 The use of these matrices in spectroscopy has led to the advent of Hadamard transform spectroscopy3 which employs spectroscopic multiplexing techniques and is a powerful tool for the analysis of complex spectra. Besides Hadamard matrices are useful in chemical designs and bloc...

We show that every weighing matrix of weight n invariant under a finite abelian group G can be generated from a subgroup H of G with |H| ≤ 2n−1. Furthermore, if n is an odd prime power and a proper circulant weighing matrix of weight n and order v exists, then v ≤ 2n−1. We also obtain a lower bound on the weight of group invariant matrices depending on the invariant factors of the underlying

We use the newly developed theory of signed groups and some known sequences with zero autocorrelation to derive new results on the asymptotic existence of Hadamard matrices. New values of t are obtained such that, for any odd number p, there exists an Hadamard matrix of order 2tp. These include: t = 2N, where N is the number of nonzero digits in the binary expansion of p, and t = 4[-~ log2((p1)...

In this paper we present infinite families of new orthogonal designs, based on some weighing matrices of order 2n, weight 2n − k and spread σ, constructed from two circulants and directed sequences.

We classify all circulant weighing matrices whose order and weight are products of powers of 2 and 3. In particular, we show that proper CW(v, 36)’s exist for all v ≡ 0 (mod 48), all of which are new.

We verify the skew weighing matrix conjecture for orders 2t .13, t 2:: 5, and give new results for 2t.15 proving the conjecture for t :2: 3.