Abstract
AbstractUsing the natural action of \(GL_2(\mathbb F_2)\simeq \frak S_3\) over \(\mathbb F_2[X]\), one can define different classes of polynomials strongly analogous to self-reciprocal irreducible polynomials. We give transformations to construct polynomials of each kind of invariance and we deal with the question of explicit infinite sequences of invariant irreducible polynomials in \(\mathbb F_2[X]\). We generalize results obtained by Varshamov, Wiedemann, Meyn and Cohen and we give sequences of invariant irreducible polynomials. Moreover we explain what happens when the given constructions fail. We also give a result on the order of the polynomials of one of the classes: the alternate irreducible polynomials.Keywordsirreducible polynomialsfinite fieldssequences of irreducible invariant polynomials
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