Preprint
Divisibility of Trinomials by Irreducible Polynomials over F_2
Zusammenfassung
Irreducible trinomials of given degree n over F_2 do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we consider some conditions under which irreducible polynomials divide trinomials over F_2. A condition for divisibility of self-reciprocal trinomials by irreducible polynomials over F_2 is established. And we extend Welch's criterion for testing if an irreducible polynomial divides trinomials x^m + x^s + 1 to the trinomials x^am + x^bs + 1.
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@article{urn:nbn:de:hebis:34-2008091623844,
author={Kim, Ryul and Koepf, Wolfram},
title={Divisibility of Trinomials by Irreducible Polynomials over F_2},
year={2008}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2008$n2008 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2008091623844 3000 Kim, Ryul 3010 Koepf, Wolfram 4000 Divisibility of Trinomials by Irreducible Polynomials over F_2 / Kim, Ryul 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2008091623844=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 08, 07 7136 ##0##urn:nbn:de:hebis:34-2008091623844
2008-09-16T07:59:06Z 2008-09-16T07:59:06Z 2008 urn:nbn:de:hebis:34-2008091623844 http://hdl.handle.net/123456789/2008091623844 47036 bytes 101226 bytes application/pdf application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Trinomial Self-reciprocal polynomial Finite field 510 Divisibility of Trinomials by Irreducible Polynomials over F_2 Preprint Irreducible trinomials of given degree n over F_2 do not always exist and in the cases that there is no irreducible trinomial of degree n it may be effective to use trinomials with an irreducible factor of degree n. In this paper we consider some conditions under which irreducible polynomials divide trinomials over F_2. A condition for divisibility of self-reciprocal trinomials by irreducible polynomials over F_2 is established. And we extend Welch's criterion for testing if an irreducible polynomial divides trinomials x^m + x^s + 1 to the trinomials x^am + x^bs + 1. open access Kim, Ryul Koepf, Wolfram Mathematische Schriften Kassel ;; 08, 07 11T06 12E05 12E20 13A05 Mathematische Schriften Kassel 08, 07
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