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Collaborative filtering is a popular recommendation technique. Although researchers have focused on the accuracy of the recommendations, real applications also need efficient algorithms. An index structure can be used to store the rating matrix and compute recommendations very fast. In this paper we study how compression techniques can reduce the size of this index structure and, at the same time, speed up recommendations. We show how coding techniques commonly used in Information Retrieval can be effectively applied to collaborative filtering, reducing the matrix size up to 75 %, and almost doubling the recommendation speed. Additionally, we propose a novel identifier reassignment technique, that achieves high compression rates, reducing by 40 % the size of an already compressed matrix. It is a very simple approach based on assigning the smallest identifiers to the items and users with the highest number of ratings, and it can be efficiently computed using a two pass indexing. The usage of the proposed compression techniques can significantly reduce the storage and time costs of recommender systems, which are two important factors in many real applications.