The autocorrelation of m-sequences over nonprime finite fields

Nonbinary m-sequences (maximal length sequences) for spread-spectrum communication systems that have a two-level autocorrelation are presented. The autocorrelation function of an m-sequence over the Galois field of q elements GF(q), where q=p/sup k/, for p a prime and k an integer greater than 1, is developed and shown to be bilevel when the elements of GF(q) are expressed as elements of a vector space over the pth roots of unity. >