One of the most important applications of finite fields has been the creation of Algebraic Coding Theory: A response to communication errors. Algebraic codes are utilized in compact disks, DVD players, fax machines, digital televisions, bar code scanners, and are crucial to computer maintenance

Algebraic Coding Theory rests on the assumption that transmission errors occur both independently from and due to human error. Minimizing the chances of such errors occurring motivates the theory.