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A new faster algorithm for factoring skew polynomials over finite fields. (English) Zbl 1373.16046
Summary: In this paper, we provide an algorithm for the factorization of skew polynomials over finite fields. It is faster than the previously known algorithm, which was due to [M. Giesbrecht, J. Symb. Comput. 26, No. 4, 463–486 (1998; Zbl 0941.68160)]. There are two main improvements. The first one is obtained through a careful study of the structure of the quotients of a skew polynomial ring, using theoretical results relating skew polynomial rings and Azumaya algebras. The second improvement is provided by giving faster sub-algorithms for the arithmetic in skew polynomial rings, such as multiplication, division, and extended Euclidean division.

16S36 Ordinary and skew polynomial rings and semigroup rings
16Z05 Computational aspects of associative rings (general theory)
16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
Full Text: DOI
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