A characterization of some finite simple groups by their character codegrees

For a finite group G and an irreducible complex character χ of G, the codegree of χ is defined by cod(χ)=|G:ker(χ)|/χ(1), where ker(χ) is the kernel of χ. 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.