In this paper, we will prove that for shaped binary sequences, the central SRS and SHG contrast ratios are closely related to the traditional Merit Factor values. And in light of known results in Merit Factor Problems, we have constructed binary sequences with large central contrast ratios, based on Legendre sequences, Parker sequences, and m-sequences, with both theoretical and numerical analysis results presented.

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.

Starting with the family of Legendre sequences of length p, Parker constructed a new family of binary sequences of length 2p with good negacyclic correlation properties. Computer calculations indicated that the asymptotic merit factor of his family is 6. In this correspondence a simple version of Parker's construction is given and further applied to Jacobi and modified Jacobi sequences. It is then proven that each of the families constructed, including Parker's, has asymptotic merit factor 6.