Many nearest neighbor search algorithms rely on encoding real vectors into binary vectors. The most common strategy projects the vectors onto random directions and takes the sign to produce so-called sketches. This paper discusses the sub-optimality of this choice, and proposes a better encoding strategy based on the quantization and reconstruction points of view. Our second contribution is a novel asymmetric estimator for the cosine similarity. Similar to previous asymmetric schemes, the query is not quantized and the similarity is computed in the compressed domain. Both our contribution leads to improve the quality of nearest neighbor search with binary codes. Its efficiency compares favorably against a recent encoding technique.