论文标题
二次扩展字段上的常规完整置换多项式
Regular complete permutation polynomials over quadratic extension fields
论文作者
论文摘要
令$ r \ geq 3 $为任何正整数，相对为$ p $和$ q^2 \ equiv 1 \ pmod r $。令$τ_1，τ_2$为$ \ mathbb {f} _ {q^2}的任何置换多项式，$ $ $σ_m$是$ \ mathbb {f} _ {q^2} $和$ c^2} $和$σ=τ_1\circcoutσ_m\ circoust $ \ mathbb {f} _ {f} _ {q^2} $。在本文中，我们证明，对于合适的$τ_1，τ_2$和$σ_m$，地图$σ$可能是$ r $ r $ remartunar-remartular完整置换多项式在二次扩展字段上。
Let $r\geq 3$ be any positive integer which is relatively prime to $p$ and $q^2\equiv 1 \pmod r$. Let $τ_1, τ_2$ be any permutation polynomials over $\mathbb{F}_{q^2},$ $σ_M$ is an invertible linear map over $\mathbb{F}_{q^2}$ and $σ=τ_1\circσ_M\circτ_2$. In this paper, we prove that, for suitable $τ_1, τ_2$ and $σ_M$, the map $σ$ could be $r$-regular complete permutation polynomials over quadratic extension fields.
