Random properties of the highest level sequences of primitive sequences over Z(2/sup e/)

Using the estimates of the exponential sums over Galois rings, we discuss the random properties of the highest level sequences (alpha)/sub e-1/ of primitive sequences generated by a primitive polynomial of degree n over Z(2/sup e/). First we obtain an estimate of 0, 1 distribution in one period of (alpha)/sub e-1/. On the other hand, we give an estimate of the absolute value of the autocorrelation function |C/sub N/(h)| of (alpha)/sub e-1/, which is less than 2/sup e-1/(2/sup e-1/-1)(radical)3(2/sup 2e/-1)2/sup n/2/+2/sup e-1/ for h(not equal)0. Both results show that the larger n is, the more random (alpha)/sub e-1/ will be.