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Using the estimates of the exponential sums over Galois rings, we discuss the random properties of the highest level sequences αe-1 of primitive sequences generated by a primitive polynomial of degree n over Z(2e). First we obtain an estimate of 0, 1 distribution in one period of αe-1. On the other hand, we give an estimate of the absolute value of the autocorrelation function |CN(h)| of αe-1, which is less than 2e-1(2e-1-1)√3(22e-1)2n2/+2e-1 for h≠0. Both results show that the larger n is, the more random αe-1 will be.