lengths is there a code that corresponds to it so let's check Kim can we find a code that matches up with this well the this thing over here is the thing that we have on the Left sent hand side into credibility and equality and we want to hopefully prove that this is smaller than one so but trying to prove it's smaller than one we have to make the steps to get there if we can prove this then it means that code exists and we're good to go we can actually means looking to enter the coding so this thing is equal to the code lengths are given by