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New Infinite Families of Orthogonal Designs Constructed from Complementary Sequences

In this paper, we present new infinite families of three and four variable orthogonal designs based on several constructions derived from complementary sequences. The above method leads to the construction of many classes of orthogonal designs. In addition, we obtain new infinite families of weighing matrices constructed by complementary sequences, such as W(144+4s,144) and W(224+4s,196) for all s ≥ 0. These families resolve the existence and construction of over 20 weighing matrices which are listed as open in the second edition of the Handbook of Combinatorial Designs.