Irreducible Polynomials Which Divide Trinomials Over GF(2). - The ...

Chapter 3The Multiplicative ModuleIn this chapter, the multiplicative module M is introduced, which is the set of positive(odd) integers t such that the irreducible polynomials of odd primitivity t > 1 dividetrinomials over GF(2). The computational results are presented, and the set G of generatorsof M is discussed.3.1 IntroductionIt is a simple fact that if the irreducible polynomials of primitivity t divide trinomials,then the irreducible polynomials of primitivity mt also divide trinomials for every oddinteger m ≥ 1. Therefore, let M be the set of positive (odd) integers t such that theirreducible polynomials of odd primitivity t > 1 divide trinomials. Then, in view of theclosure property, we call M a multiplicative module. That is, for every t ∈ M, we alsohave mt ∈ M for every odd integer m ≥ 1.An element g of M is a generator of M if and only if g ∈ M but no proper factor h ofg is in M. Let G be the subset of M consisting of the generators of M. From Theorem30