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22 March 2025

» arxiv » 2201.00108

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The Mathieu group $M_{23}$ as additive functions on the finite field of size ${2^{11}}$
Yiming Bing ; Bright Hu ; Ronni Hu ; Rhianna Li ; Stefan Lu ; Finn McDonald ; Michael Sun ; Nicholas Wolfe ; Joshua Yao ; Leon Zhou ; Nathan Zhou ;
Date:	1 Jan 2022
Abstract:	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 $varphi:mathbb{F}_{2^{11}} o mathbb{F}_{2^{11}}$ such that $varphi(x+y)=varphi(x)+varphi(y)$ and $varphi\|_{C}$ is the standard permutation action. We give explicit $11 imes 11$ matrices for the pair of standard generators of order $23$ and order $5$, as well as many tables to help facilitate future calculations.
Source:	arXiv, 2201.00108
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