Some algorithms for skew polynomials over finite fields

Abstract : In this paper, we study the arithmetics of skew polynomial rings over finite fields, mostly from an algorithmic point of view. We give various algorithms for fast multiplication, division and extended Euclidean division. We give a precise description of quotients of skew polynomial rings by a left principal ideal, using results relating skew polynomial rings to Azumaya algebras. We use this description to give a new factorization algorithm for skew polynomials, and to give other algorithms related to factorizations of skew polynomials, like counting the number of factorizations as a product of irreducibles.
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Contributor : Xavier Caruso <>
Submitted on : Friday, December 14, 2012 - 8:59:09 PM
Last modification on : Thursday, November 15, 2018 - 11:56:36 AM
Document(s) archivé(s) le : Friday, March 15, 2013 - 3:53:15 AM


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  • HAL Id : hal-00765577, version 1
  • ARXIV : 1212.3582


Xavier Caruso, Jérémy Le Borgne. Some algorithms for skew polynomials over finite fields. 2012. ⟨hal-00765577⟩



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