Analysis and synthesis of polynomials and sequences overGF(2)
Abraham Lempel · IEEE Transactions on Information Theory · 1971
The analysis and synthesis of polynomials and sequences overGF(2)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 ofGF(2^n). For each value ofnthe cyclonomials are determined by the partition of the set\{ 0,1,2, \cdots ,2^n - 2 \}into cyclotomic cosets. A method of deriving all primitive polynomials of degreenfrom 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.