A class of permutation trinomials over finite fields

• Autorzy: Xiang-dong Hou
• Języki publikacji: EN

Abstrakty

EN

Let q > 2 be a prime power and $f = -x + tx^{q} + x^{2q-1}$, where $t ∈ 𝔽*_{q}$. We prove that f is a permutation polynomial of $𝔽_{q²}$ if and only if one of the following occurs: (i) q is even and $Tr_{q/2}(1/t) = 0$; (ii) q ≡ 1 (mod 8) and t² = -2.

Kategorie tematyczne

• 11T55: Arithmetic theory of polynomial rings over finite fields
• 11T06: Polynomials

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 162
• Numer: 1
• Strony: 51-64

Daty

wydano

2014

Twórcy

autor

Xiang-dong Hou

• Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, U.S.A.

Identyfikatory

DOI

10.4064/aa162-1-3