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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. Index Terms--Aperiodic correlation, Jacobi sequence, Legendre sequence, merit factor.

In this correspondence, we first establish a strong limit theorem for countable nonhomogeneous Markov chains indexed by a homogeneous tree. As corollaries, we obtain some strong limit theorems for frequencies of occurrence of states and ordered couple of states for this Markov chains. Finally, we prove the strong law of large numbers and the asymptotic equipartition property (AEP) for finite nonhomogeneous Markov chains indexed by a homogeneous tree. Index Terms--Asymptotic equipartition property, homogeneous tree, nonhomogeneous Markov chains.