La factorisation de $x^{p^l}-x\in{\mathbb F}\_p[x]$ selon la trace

Roland Bacher

La factorisation de $x^{p^l}-x\in{\mathbb F}\_p[x]$ selon la trace

Number Theory 2007-05-23 v1

Authors: Roland Bacher

Abstract

We present a few factorizations of polynomials over finite fields. These factorizations are related to traces, compositions of polynomials and binomial coefficients. As a corollary we obtain a description of all irreducible polynomials $Q\in {\mathbb F}\_2[x]$ such that $Q(1+x+x^2)$ (or $Q(x+x^2)$ ) remain irreducible.

Keywords

polynomials over finite fields polynomial theory finite fields

Cite

@article{arxiv.math/0607413,
  title  = {La factorisation de $x^{p^l}-x\in{\mathbb F}\_p[x]$ selon la trace},
  author = {Roland Bacher},
  journal= {arXiv preprint arXiv:math/0607413},
  year   = {2007}
}

Comments

6 pages

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