The mathematical properties of high-dimensional (HD) spaces show remarkable agreement with behaviors controlled by the brain. Computing with HD vectors, referred to as "hypervectors," is a brain-inspired alternative to computing with numbers. HD computing is characterized by generality, scalability, robustness, and fast learning, making it a prime candidate for utilization in application domains such as brain-computer interfaces. We describe the use of HD computing to classify electroencephalography (EEG) error-related potentials for noninvasive brain-computer interfaces. Our algorithm encodes neural activity recorded from 64 EEG electrodes to a single temporal-spatial hypervector. This hypervector represents the event of interest and is used for recognition of the subject's intentions. Using the full set of training trials, HD computing achieves on average 5% higher accuracy compared to a conventional machine learning method on this task (74.5% vs. 69.5%) and offers further advantages: (1) Our algorithm learns fast by using 34% of training trials while surpassing the conventional method with an average accuracy of 70.5%. (2) Conventional method requires prior domain expert knowledge to carefully select a subset of electrodes for a subsequent pre-processor and classier, whereas our algorithm blindly uses all 64 electrodes, tolerates noises in data, and the resulting hypervector is intrinsically clustered into HD space; in addition, most preprocessing of the electrode signal can be eliminated while maintaining an average accuracy of 71.7%.