dc.date.accessioned 2008-05-26T11:44:49Z dc.date.available 2008-05-26T11:44:49Z dc.date.issued 2008 dc.identifier.uri urn:nbn:de:hebis:34-2008052621729 dc.identifier.uri http://hdl.handle.net/123456789/2008052621729 dc.format.extent 214348 bytes dc.format.mimetype application/pdf dc.language.iso eng dc.subject Finite field eng dc.subject Irreducible polynomials eng dc.subject Type II pentanomials eng dc.subject.ddc 510 dc.title The Parity of the Number of Irreducible Factors for Some Pentanomials eng dc.type Preprint dcterms.abstract It 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, eng 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. dcterms.accessRights open access dcterms.creator Koepf, Wolfram dcterms.creator Kim, Ryul dcterms.isPartOf Mathematische Schriften Kassel ger dcterms.isPartOf 08, 05 ger
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