Further results on ternary complementary sequences, orthogonal designs and weighing matrices

A set of sequences is complementary, if the sum of their periodic or nonperiodic autocorrelation function is zero. Infinite families of orthogonal designs, based on some weighing matrices of order 2n, weight 2n− k and spread σ, are constructed from two circulants matrices by using complementary sequences of zero non-periodic autocorrelation function, i.e. ternary complementary pairs. Moreover, a new measure is introduced, called ζ-efficiency, for ternary complementary pairs and some of its basic properties are explored. Using the notion of ζ-efficiency, some infinite classes of weighing matrices from ternary complementary pairs are constructed. Finally, a multiplication theorem for sequences with zero periodic autocorrelation function is given and its consequences are studied. As an application, we give some more weighing matrices from the derived pairs of zero periodic autocorrelation function.