Determination of a type of permutation trinomials over finite fields

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

Abstrakty

EN

Let $f = ax + bx^q + x^{2q-1} ∈ 𝔽_q[x]$. We find explicit conditions on a and b that are necessary and sufficient for f to be a permutation polynomial of $𝔽_{q²}$. This result allows us to solve a related problem: Let $g_{n,q} ∈ 𝔽_p[x]$ (n ≥ 0, $p = char 𝔽_q$) be the polynomial defined by the functional equation $∑_{c∈ 𝔽_q} (x+c)^n = g_{n,q} (x^q -x)$. We determine all n of the form $n = q^α - q^β - 1$, α > β ≥ 0, for which $g_{n,q}$ is a permutation polynomial of $𝔽_{q²}$.

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: 166
• Numer: 3
• Strony: 253-278

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/aa166-3-3