0, 1 distribution in the highest level sequences of primitive sequences over

Abstract

In this paper, we discuss the 0,1 distribution in the highest level sequence a e -1 of primitive sequence over Z 2 e generated by a primitive polynomial of degree n . First we get an estimate of the 0,1 distribution by using the estimates of exponential sums over Galois rings, which is tight for e relatively small to n . We also get an estimate which is suitable for e relatively large to n . Combining the two bounds, we obtain an estimate depending only on n , which shows that the larger n is, the closer to 1/2 the proportion of 1 will be.