Some results on Kharaghani type orthogonal designs

In this paper we give a general theorem which can be used to multiply the length of amicable sequences keeping the amicability property and the type of the sequences. As a consequence we have that if there exist two, four or eight amicable sequences of length m and type (al, a2), (al, a2, a3, a4) or (al, a2, …, as) then there exist amicable sequences of length ℓ ≡ 0 (mod m) and of the same type. We also present a theorem that produces a set of 2v amicable sequences from a set of v (not necessary amicable) sequences and a construction method for amicable sequences of type (al, al, a2, a2, ... , av, av) from v pairs of disjoint (0, ±1) amicable sequences. Using these results we can obtain many infinite classes of Kharaghani type orthogonal designs. Actually, if there exists an Kharaghani type orthogonal design of order n and of type (al, a2, …, av), which is constructed from sequences, then there exists an infinite family of Kharaghani type orthogonal designs of the same type which is constructed from appropriate sequences.