Analysis and synthesis of polynomials and sequences over

The analysis and synthesis of polynomials and sequences over has received considerable attention in recent years with the increasing use of PN sequences. In this paper a new approach to the problem is presented in which the polynomial coefficients and the sequence digits are derived in terms of the values assumed by a special class of polynomials, called "cyclonomials," at an arbitrary primitive element of . For each value of the cyclonomials are determined by the partition of the set into cyclotomic cosets. A method of deriving all primitive polynomials of degree from a given one of the same degree is described. A short outline of an approach to the more difficult task of synthesizing an initial primitive polynomial is also presented.