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.