This thesis is centered around one of the most basic information retrieval problems, namely that of storing and accessing the elements of a set. Each element in the set has some associated information that is returned along with it. The problem is referred to as the dictionary problem, due to the similarity to a bookshelf dictionary, which contains a set of words and has an explanation associated with each word. In the static version of the problem the set is fixed, whereas in the dynamic version, insertions and deletions of elements are possible. The approach

We deal with the problem of storing a set of K elements that are taken from a large universe of size N , such that membership in the set can be determined with high probability by looking at just one bit of the representation. Buhrman et al. show an explicit construction with about K log N storing bits. We show an explicit construction with about K storing bits, that gets closer to the optimal K log N bound.