Modifications of Modified Jacobi Sequences

The known families of binary sequences having asymptotic merit factor 6.0 are modifications to the families of Legendre sequences and Jacobi sequences. In this paper, we show that at N = pq, there are many suitable modifications other than the Jacobi or modified Jacobi sequences. Furthermore, we will give three new modifications to the character sequences of length N = pq. Based on these new modifications, for any pair of large p and q, we can construct a binary sequence of length 2pq so that such families of sequences have asymptotic merit factor 6.0 without cyclic shifting of the base sequences.