The P300 speller is a brain-computer interface that enables people with severe neuromuscular disorders to communicate. It is based on eliciting and detecting event-related potentials (ERP) in electroencephalography (EEG) measurements, in response to rare target stimulus events. One of the challenges to fast and reliable communication is the fact that the P300-based ERP has a refractory period that induces temporal dependence in the user's EEG responses. Refractory effects negatively affects the performance of the speller. The contribution of this paper is to provide a model for the P300 speller as a communication process with memory to account for refractory effects. Using this model, we design codebooks that maximize the mutual information rate between the user's desired characters and the measured EEG responses to the stimulus events. We show simulation results that compare our codebook with other codebooks described in literature.