Journal article
Divisibility of trinomials by irreducible polynomials over F2
Publication Details
Authors: | Koepf, W.; Kim, R. |
Publication year: | 2009 |
Journal: | International Journal of Algebra |
Pages range : | 189-197 |
Volume number: | 3 |
ISSN: | 1312-8868 |
eISSN: | 1312-8868 |
URN / URL: |
Abstract
Irreducible trinomials of given degree n over F2 do not always exist andin the cases that there is no irreducible trinomial of degree n it may be effectiveto use trinomials with an irreducible factor of degree n. In this paperwe consider some conditions under which irreducible polynomials divide trinomialsover F2. A condition for divisibility of self-reciprocal trinomials byirreducible polynomials over F2 is established. And we extend Welch's criterionfor testing if an irreducible polynomial divides trinomials x^m +x^s +1 tothe trinomials x^{am} + x^{bs} + 1.
Irreducible trinomials of given degree n over F2 do not always exist andin the cases that there is no irreducible trinomial of degree n it may be effectiveto use trinomials with an irreducible factor of degree n. In this paperwe consider some conditions under which irreducible polynomials divide trinomialsover F2. A condition for divisibility of self-reciprocal trinomials byirreducible polynomials over F2 is established. And we extend Welch's criterionfor testing if an irreducible polynomial divides trinomials x^m +x^s +1 tothe trinomials x^{am} + x^{bs} + 1.
