In this thesis, we analyze the Kraft Inequality and the Kraft-McMillan Inequality in their equality cases. Kraft’s Inequality deals with prefix-free code and Kraft-McMillan’s Inequality deals with uniquely decodable codes. The focus of the Kraft Inequality analysis is to study the occurrence of prefix-free codes that satisfy the equality case and the structure of words in the code when the equality condition is met. The second part of the thesis touches on the Kraft-McMillan Inequality. Since the proof of this latter inequality uses limits, we cannot immediately analyse its equality cases. The paper will therefore study the equality cases of this theorem and demonstrate that these equality cases have similar results to that of the Kraft Inequality, although it is necessary to prove them in a different way since the latter theorem’s proof is less direct
