Determination of a type of permutation trinomials over finite fields

Xiang-dong Hou. "Determination of a type of permutation trinomials over finite fields." Acta Arithmetica 166.3 (2014): 253-278. <http://eudml.org/doc/279147>.

@article{Xiang2014,
abstract = {Let $f = ax + bx^q + x^\{2q-1\} ∈ _q[x]$. We find explicit conditions on a and b that are necessary and sufficient for f to be a permutation polynomial of $_\{q²\}$. This result allows us to solve a related problem: Let $g_\{n,q\} ∈ _p[x]$ (n ≥ 0, $p = char _q$) be the polynomial defined by the functional equation $∑_\{c∈ _q\} (x+c)^n = g_\{n,q\} (x^q -x)$. 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 $_\{q²\}$.},
author = {Xiang-dong Hou},
journal = {Acta Arithmetica},
keywords = {discriminant; finite field; permutation polynomial},
language = {eng},
number = {3},
pages = {253-278},
title = {Determination of a type of permutation trinomials over finite fields},
url = {http://eudml.org/doc/279147},
volume = {166},
year = {2014},
}

TY - JOUR
AU - Xiang-dong Hou
TI - Determination of a type of permutation trinomials over finite fields
JO - Acta Arithmetica
PY - 2014
VL - 166
IS - 3
SP - 253
EP - 278
AB - Let $f = ax + bx^q + x^{2q-1} ∈ _q[x]$. We find explicit conditions on a and b that are necessary and sufficient for f to be a permutation polynomial of $_{q²}$. This result allows us to solve a related problem: Let $g_{n,q} ∈ _p[x]$ (n ≥ 0, $p = char _q$) be the polynomial defined by the functional equation $∑_{c∈ _q} (x+c)^n = g_{n,q} (x^q -x)$. 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 $_{q²}$.
LA - eng
KW - discriminant; finite field; permutation polynomial
UR - http://eudml.org/doc/279147
ER -