论文标题
MATHIEU组$ M_ {23} $作为大小$ {2^{11}} $的有限字段上的加法功能
The Mathieu group $M_{23}$ as additive functions on the finite field of size ${2^{11}}$
论文作者
论文摘要
我们明确地扩展了23个元素上的Mathieu组$ M_ {23} $的标准排列操作$ C = C = C = C_ {23} $包含在$ 2^{11} $ elements $ \ Mathbb {f} _ {2^{11}} $上的有限字段中，以在此有限的字段上进行附加功能。也就是说，我们代表$ m_ {23} $作为函数$φ：\ mathbb {f} _ {2^{11}}} \ to \ mathbb {f} _ {2^{11}} $我们给出了一对订单$ 23 $和订单$ 5 $的标准生成器的明确$ 11 $矩阵，以及许多表，以帮助促进未来的计算。
We explicitly extend the standard permutation action of the Mathieu group $M_{23}$ on a 23 element set $C=C_{23}$ contained in a finite field of $2^{11}$ elements $\mathbb{F}_{2^{11}}$ to additive functions on this finite field. That is we represent $M_{23}$ as functions $φ:\mathbb{F}_{2^{11}}\to \mathbb{F}_{2^{11}}$ such that $φ(x+y)=φ(x)+φ(y)$ and $φ|_{C}$ is the standard permutation action. We give explicit $11\times 11$ matrices for the pair of standard generators of order $23$ and order $5$, as well as many tables to help facilitate future calculations.
