论文标题
$ \ bbb f_ {q^2} $的置换多项式的一般结构
A General Construction of Permutation Polynomials of $\Bbb F_{q^2}$
论文作者
论文摘要
令$ r $为正整数，$ h（x）\ in \ bbb f_ {q^2} [x] $，$μ_{q+1} $是订单$ q+q+1 $ of $ \ bbb f_ \ bbb f_ {q^2}^*$的子组。众所周知，$ x^rh（x^{q-1}）$ permerutes $ \ bbb f_ {q^2} $，仅当$ \ text {gcd}（gcd}（r，q-1）= 1 $和$ x^rh（x）此类类型的$ \ bbb f_ {q^2} $的置换多项式有许多临时构造，因此$ h（x）^{q-1} $在$μ__{q+1} $的子组的coset上诱导了单个功能。我们提供了一个通用结构，该构造可以通过算法，{\ em all} $ \ bbb f_ {q^2} $的{\ em all}置换多项式使用，其中包括许多以前未知的属性。对于置换二项式和三项式，明确说明了该结构。
Let $r$ be a positive integer, $h(X)\in\Bbb F_{q^2}[X]$, and $μ_{q+1}$ be the subgroup of order $q+1$ of $\Bbb F_{q^2}^*$. It is well known that $X^rh(X^{q-1})$ permutes $\Bbb F_{q^2}$ if and only if $\text{gcd}(r,q-1)=1$ and $X^rh(X)^{q-1}$ permutes $μ_{q+1}$. There are many ad hoc constructions of permutation polynomials of $\Bbb F_{q^2}$ of this type such that $h(X)^{q-1}$ induces monomial functions on the cosets of a subgroup of $μ_{q+1}$. We give a general construction that can generate, through an algorithm, {\em all} permutation polynomials of $\Bbb F_{q^2}$ with this property, including many which are not known previously. The construction is illustrated explicitly for permutation binomials and trinomials.
