A method for creating a high efficiency, error minimizing code is provided. In addition, an apparatus having a high efficiency, error minimizing code is provided. In particular, the present invention provides a high efficiency, error minimizing code for use in connection with systems having a communication channel in which identifiable dominant errors occur, and that is used to transmit data that may be usefully applied in the system even though the received signal is not exactly equal to the original signal. Furthermore, the present invention provides a code that may be used to constrain the effects of dominant errors in a communication channel.