A characterization of some finite simple groups by their character codegrees

For a finite group $G$ and an irreducible complex character $\chi$ of $G$, the codegree of $\chi$ is defined by $\textrm{cod}(\chi)=|G:\textrm{ker}(\chi)|/\chi(1)$, where $\textrm{ker}(\chi)$ is the kernel of $\chi$. In this paper, we show that if $H$ is a finite simple exceptional group of Lie type or a 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.