In computer science and information theory, the issue of error correction and detection has great practical importance. Error detection is the ability to detect errors that are made due to noise or other impairments in the course of the transmission from the transmitter to the receiver. Error correction has the additional feature that enables localization of the errors and correcting them. Given the goal of error correction, the idea of error detection may seem to be insufficient. However, error-correction schemes may be computationally intensive, or require excessive redundant data which may be inhibitive for a certain application. Error correction in some applications, such as a sender-receiver system, can be achieved with only a detection system in tandem with an automatic repeat request scheme to notify the sender that a portion of the data sent was received incorrectly and will need to be retransmitted, however where efficiency is important, it is possible to detect and correct errors with far less redundant data.