An introduction to binary sequences, combinatorial designs and how they are related to communication theory and computer security is given. An exhaustive search algorithm for normal sequences is presented. This is the first time that the lengths n = 24 and n = 25 have been searched through completely. No sequences of length 24 are found. It turns out that all the normal sequences of length 25 can be derived from Turyn sequences. This construction is subject to a new theorem that is given here.