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2015•Unpublished venueRequires access

On the Primitivity of Some Trinomials Over Finite Fields

Yujuan Li, Huaifu Wang, Zhao Jinhua

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Abstract

In this paper, we give conditions under which the trinomials of the form xn + ax+ b over finite field Fpm are not primitive and conditions under which there are no primitive trinomials of the form xn + ax + b over finite field Fpm . Specially for finite field F4, we show that the trinomials of the form xn + ax + b can not be primitive over F4 except possibly for n = 2, n ≡ 5 (mod 30) or n ≡ 11 (mod 30).

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What this paper is about

In this paper, we give conditions under which the trinomials of the form xn + ax+ b over finite field Fpm are not primitive and conditions under which there are no primitive trinomials of the form xn + ax + b over finite field Fpm . Specially for finite field F4, we show that the trinomials of the form xn + ax + b can not be primitive over F4 except possibly for n = 2, n ≡ 5 (mod 30) or n ≡ 11 (mod 30).

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Available abstract

In this paper, we give conditions under which the trinomials of the form xn + ax+ b over finite field Fpm are not primitive and conditions under which there are no primitive trinomials of the form xn + ax + b over finite field Fpm . Specially for finite field F4, we show that the trinomials of the form xn + ax + b can not be primitive over F4 except possibly for n = 2, n ≡ 5 (mod 30) or n ≡ 11 (mod 30).

Key concepts: Trinomial, Finite field, Mathematics, Field (mathematics), Combinatorics, Discrete mathematics, Pure mathematics

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