On sequences with zero autocorrelation and orthogonal designs

We propose some methods for multiplying the length and type of sequences wi th elements on a set of commuting variables which have zero non-periodic au tocorrelation function. We use base sequences of lengths n + 1, n + 1, n, n in order to construct four directed sequences of lengths n + 1, n + 1, n,n and type (2n + 1, 2n + 1) with zero NPAF as well as normal sequences of le ngth n in order to construct four directed sequences of length 2n and type (2n, 2n, 2n, 2n) with zero NPAF. We construct two and four directed sequenc es with zero PAF of length 34 and type (34, 34), and (34, 34, 34, 34), resp ectively, as well as four directed sequences with zero NPAF of lengths 34, 34, 33, 33 and type (67,67). We also indicate that from m directed sequence s of lengths n(1), n(2),..., n(m), which consist of t variables, we obtain k.m directed sequences of lengths n(1), n(2),..., n(m) (k sequences will be of lengths n(i), i = 1, 2,..., m) which consist of k.t variables for k = 1 , 2,.... The above methods lead to the construction of many new orthogonal designs. (C) 2001 Academic Press.