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Transformations on Irreducible Binary Polynomials

  • Jean-Francis Michon
  • Philippe Ravache
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6338)

Abstract

Using 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.

Keywords

irreducible polynomials finite fields sequences of irreducible invariant polynomials 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jean-Francis Michon
    • 1
  • Philippe Ravache
    • 1
  1. 1.LITIS EA 4108Université de RouenSaint-Étienne du Rouvray cedexFrance

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