an:06320628
Zbl 1297.11148
Yuan, Pingzhi; Ding, Cunsheng
Further results on permutation polynomials over finite fields
EN
Finite Fields Appl. 27, 88-103 (2014).
00334886
2014
j
11T06 05B10
permutation polynomials; linearized polynomials; skew Hadamard difference sets
Let \(\mathbb F_{q^n}\) be a finite field. The main result of the paper is: Suppose \(g(x)\in\mathbb F_{q^n}[x]\) satisfies \(g(x)^q=g(x)\) for all \(x\in \mathbb F_{q^n}\), and let \(L(x)\) be a linearized polynomial. For every \(\delta\in \mathbb F_{q^n}\),
\[
f(x)=g(x^q-x+\delta)+L(x)
\]
permutes \(\mathbb F_{q^n}\) if and only if \(L(x)\) does. The authors use this to unify some previous constructions of permutation polynomials and to construct new ones.
Typos have been corrected in the corrigenda [ibid. 30, 153--154 (2014; Zbl 1297.11150)].
Robert Fitzgerald (Carbondale)
Zbl 1297.11150