系数位于子域中的线性置换多项式的新结果
New results on linear permutation polynomials with coefficients in a subfield
AI总结：
研究系数限定于子域的有限域线性置换多项式，利用商环上一般线性群子群的同构像刻画其族、计算规模，并给出 F_{q^{2p}} 情形的构造准则。
摘要：
本文通过系数条件，明确刻画了若干族系数在 F_{q^m} 中的 F_{q^{ms}} 线性置换多项式；这些族被表示为环 F_q[x]/⟨x^s−1⟩ 上 m 次一般线性群中经典子群的同构像。此外，文中计算了其中若干族的大小。最后，给出了若干准则，用于构造 F_{q^{2p}}（其中 p 为素数）上在 F_{q^2} 中具有指定系数的线性置换多项式，并给出说明主要结果的例子。
英文摘要：
Some families of linear permutation polynomials of $\mathbb{F}_{q^{ms}}$ with coefficients in $\mathbb{F}_{q^{m}}$ are explicitly described (via conditions on their coefficients) as isomorphic images of classical subgroups of the general linear group of degree $m$ over the ring $\frac{\mathbb{F}_{q}[x]}{\left\langle x^{s}-1 \right\rangle}$. In addition, the sizes of some of these families are computed. Finally, several criteria to construct linear permutation polynomials of $\mathbb{F}_{q^{2p}}$ (where $p$ is a prime number) with prescribed coefficients in $\mathbb{F}_{q^{2}}$ are given. Examples illustrating the main results are presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
