Construction of Even Length Binary Sequences With Asymptotic Merit Factor $6$

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.