Preprint
The Parity of the Number of Irreducible Factors for Some Pentanomials
Zusammenfassung
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,
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.
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.
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@article{urn:nbn:de:hebis:34-2008052621729,
author={Koepf, Wolfram and Kim, Ryul},
title={The Parity of the Number of Irreducible Factors for Some Pentanomials},
year={2008}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2008$n2008 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2008052621729 3000 Koepf, Wolfram 3010 Kim, Ryul 4000 The Parity of the Number of Irreducible Factors for Some Pentanomials / Koepf, Wolfram 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2008052621729=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 08, 05 7136 ##0##urn:nbn:de:hebis:34-2008052621729
2008-05-26T11:44:49Z 2008-05-26T11:44:49Z 2008 urn:nbn:de:hebis:34-2008052621729 http://hdl.handle.net/123456789/2008052621729 214348 bytes application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Finite field Irreducible polynomials Type II pentanomials 510 The Parity of the Number of Irreducible Factors for Some Pentanomials Preprint 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, 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. open access Koepf, Wolfram Kim, Ryul Mathematische Schriften Kassel ;; 08, 05 Mathematische Schriften Kassel 08, 05
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