Aufsatz in einer Fachzeitschrift
The parity of the number of irreducible factors for some pentanomials
Details zur Publikation
Autor(inn)en: | Koepf, W.; Kim, R. |
Publikationsjahr: | 2009 |
Zeitschrift: | Finite Fields and Their Applications |
Seitenbereich: | 585-603 |
Jahrgang/Band : | 15 |
Heftnummer: | 5 |
Erste Seite: | 585 |
Letzte Seite: | 603 |
ISSN: | 1071-5797 |
eISSN: | 1090-2465 |
DOI-Link der Erstveröffentlichung: |
Zusammenfassung, Abstract
It is well known that the Stickelberger-Swan theorem is very important for determining the reducibility of polynomials over a binary field. Using this theorem 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 was determined. We discuss this problem for Type II pentanomials, namely x(m) + x(n+2) + x(n+1) + x(n) + 1 is an element of F-2[x] for even m. Such pentanomials can be used for the e. cient implementation of multiplication in finite fields of characteristic two. Based on the computation of the discriminant of these pentanomials with integer coefficients, we will characterize the parity of the number of irreducible factors over F2 and establish necessary conditions for the existence of this kind of irreducible pentanomials. Our results have been obtained in an experimental way by computing a significant number of values with Mathematica and extracting the relevant properties. (C) 2009 Elsevier Inc. All rights reserved.
It is well known that the Stickelberger-Swan theorem is very important for determining the reducibility of polynomials over a binary field. Using this theorem 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 was determined. We discuss this problem for Type II pentanomials, namely x(m) + x(n+2) + x(n+1) + x(n) + 1 is an element of F-2[x] for even m. Such pentanomials can be used for the e. cient implementation of multiplication in finite fields of characteristic two. Based on the computation of the discriminant of these pentanomials with integer coefficients, we will characterize the parity of the number of irreducible factors over F2 and establish necessary conditions for the existence of this kind of irreducible pentanomials. Our results have been obtained in an experimental way by computing a significant number of values with Mathematica and extracting the relevant properties. (C) 2009 Elsevier Inc. All rights reserved.
