We describe a new approach for classification with a very large number of classes where we assume some class similarity information is available, e.g. through a hierarchical organization. The proposed method learns a compact binary code using such an existing similarity information defined on classes. Binary classifiers are then trained using this code and decoding is performed using a simple nearest neighbor rule. This strategy, related to Error Correcting Output Codes methods, is shown to perform similarly or better than the standard and efficient one-vs-all approach, with much lower inference complexity.