Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895714 | Finite Fields and Their Applications | 2018 | 14 Pages |
Abstract
Let f(x)âFq[x] be an irreducible polynomial of degree m and exponent e. For each positive integer n, such that νp(qâ1)â¥Î½p(e)+νp(n) for all prime divisors p of n, we show a fast algorithm to determine the irreducible factors of f(xn). Using this algorithm, we give the complete factorization of xnâ1 into irreducible factors in the case where n=dpt, p is an odd prime, q is a generator of the group Zp2â and either d=2m with mâ¤Î½2(qâ1) or d=ra, where r is a prime dividing qâ1 but not pâ1.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
F.E. Brochero MartÃnez, Lucas Reis,