Prevent pushes to git containing tabs in certain files (e.g. *.cpp, *.h, CMakeLists.txt)

I'd like my remote repository to refuse any pushes that contains a file that contains a tab, but only if the file belongs in a certain class (based on the filename). Is that possible?
I have looked a bit at the update hook in githooks, and I think that is the correct one.

So in short, a push should be rejected if:

1. there is a file of the listed types (*.cpp, *.h, CMakeLists.txt)
2. that contains one or more tab characters.