The purpose of this study is to develop a new methodology for designing stimulus sequences for Brain Computer Interfaces that utilize code modulated Visually Evoked Potentials (cVEP BCIs), based on experimental results regarding the behavior and the properties of the actual EEG responses of the visual system to binary-coded visual stimuli, such that training time is reduced and possible number of targets is increased. EEG from 8 occipital sites is recorded with 2000 sps, in response to visual stimuli presented on a computer monitor with 60 Hz refresh rate. EEG responses of the visual system to black-to-white and white-to-black transitions of a target area on the monitor are recorded for 500 ms, for 160 trials, and signal-averaged to obtain the onset (positive edge) and offset (negative edge) responses, respectively. It is found that both edge responses are delayed by 50 ms and wane completely within 350 ms. These edge responses are then used to generate (predict) the EEG responses to arbitrary binary stimulus sequences using the superposition principle. It is found that the generated and the measured EEG responses to certain (16) simple short sequences (16.67-350 ms) are highly correlated. These 'optimal short patterns' are then randomly combined to design the long (120 bit, 2 sec) 'Superposition Optimized Pulse (SOP)' sequences, and their EEG response templates are obtained by superposition of the edge responses. A SOP sequence-based Visual Speller BCI application yielded higher accuracy (95.9%) and Information Transfer Rate (ITR) (57.2 bpm), compared to when superposition principle is applied to conventional m-sequences and randomly generated sequences. Training for the BCI application involves only the acquisition of the edge responses and takes less than 4 min. This is the first study in which the EEG templates for cVEP BCI sequences are obtained by the superposition of edge responses.