A characterization of some finite simple groups by their character codegrees

Let $G$ be a finite group and let $\chi$ be a complex irreducible character of $G$. The codegree of $\chi$ is defined by $\mathrm{cod}\left(\chi \right)=|G:\ker (\chi \left)\right|/\chi \left(1\right)$, where $\ker \left(\chi \right)$ is the kernel of $\chi$. In this paper, we show that if $H$ is a finite simple exceptional group of Lie type or a finite simple projective special linear group and $G$ is any finite group such that the character codegree sets of $G$ and $H$ coincide, then $G$ and $H$ are isomorphic.