On Sequences with Zero Autocorrelation and Orthogonal Designs

We propose some methods for multiplying the length and type of sequences with elements on a set of commuting variables which have zero non-periodic autocorrelation 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 length 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 sequences with zero PAF of length 34 and type (34, 34), and (34, 34, 34, 34), respectively, 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 sequences of lengths n1, n2, …, nm which consist of t variables, we obtain k·m directed sequences of lengths n1, n2, …, nm (k sequences will be of lengths ni, 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.