Associative memories are devices that are able to learn messages and to retrieve them in presence of errors or erasures. Their mecanics is similar to the one of error decoders. However, the role of correlation is opposed in the two devices, used as the essence of the retrieval process in the first one and avoided in the second one. Original codes are introduced in this paper to allow the effective combination of the two domains. The main idea is to associate with each message to learn a clique in a binary neural network. The obtained performance is dramatically better than the one corresponding to the state of the art, for instance Hopfield Neural Networks. Moreover, the model proposed is biologically plausible: it uses binary sparse connections between clusters of neurons provided with only two operations: sum and selection of maximum.