Generation of linear recursive sequences from irreducible polynomials over GF(Q)

Linear recursive sequences generated from irreducible polynomials over GF(q), q=P^m, a prime power, are investigated. These sequences are expressed as vector linear recursive sequences whose component sequences may be obtained directly from an irreducible polynomial over GF(p). The relationship between these components is investigated. A method of generating the primitive and nonprimitive irreducible polynomials is also discussed