The Miracle Octad Generator is a 4x6 array of combinations describing any point in 24-dimensional space.
Another use for the Miracle Octad Generator is to quickly verify codewords of the binary Golay code.
Each element of the Miracle Octad Generator can store either a '1' or a '0', usually displayed as an asterisk and blank space, respectively.
Each column and the top row have a property known as the count, which is the number of asterisks in that particular line.
One of the criteria for a set of 24 coordinates to be a codeword in the binary Golay code is for all seven counts to be of the same parity.