Is there carpet at this doorway?

Sometimes the carpet has a seam at the doorway, or if not can at least be pulled up enough to sneak the ethernet cable under it.

I've successfully run ethernet, telephone, and TV cable wires in the little gap between the wall and the carpet tack strip. Sometimes you don't even need to pull up the carpet to do it, just get a big screwdriver and poke the cable into the gap; there's a little resistance and then FOOMP the cable disappears into the gap. (Don't use your fingers, those carpet tack strips are sharp if you push too hard.) When you get to the doorway, you have to pull up the carpet there but you're essentially doing the same thing. Sometimes you have to make a gap in the carpet tack strip at the meeting point between the door transom and the tack strip, because the cable is essentially going from one side of a tack strip to the other at that point.