Crosscorrelation of m-sequences over nonprime finite fields

The crosscorrelation function of m-sequences over GF(q) where q=p^m, p a prime and m an integer greater than 1 is developed. This crosscorrelation function is shown to have three and four levels similar to the case of m-sequences over GF(p) (a prime field) when the elements of GF(q) are expressed as elements of a vector space over the pth roots of unity. These nonbinary m-sequences can improve performance over binary m-sequences in spread spectrum and code division multiple access communications systems.