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dc.subjectFinite fieldeng
dc.subjectIrreducible polynomialseng
dc.subjectType II pentanomialseng
dc.titleThe Parity of the Number of Irreducible Factors for Some Pentanomialseng
dcterms.abstractIt is well known that Stickelberger-Swan theorem is very important for determining reducibility of polynomials over a binary field. Using this theorem it was determined the parity of the number of irreducible factors for some kinds of polynomials over a binary field, for instance, trinomials, tetranomials, self-reciprocal polynomials and so on. We discuss this problem for type II pentanomials namely x^m +x^{n+2} +x^{n+1} +x^n +1 \in\ IF_2 [x]. Such pentanomials can be used for efficient implementing multiplication in finite fields of characteristic two. Based on the computation of discriminant of these pentanomials with integer coefficients, it will be characterized the parity of the number of irreducible factors over IF_2 and be established the necessary conditions for the existence of this kind of irreducible pentanomials.eng
dcterms.accessRightsopen access
dcterms.creatorKoepf, Wolfram
dcterms.creatorKim, Ryul
dcterms.isPartOfMathematische Schriften Kasselger
dcterms.isPartOf08, 05ger

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