Z₄-linear codes

Coding theory is a branch of mathematics that began in the 1940's to correct errors caused by noise in communication channels. It is know that certain nonlinear codes satisfy the MacWilliams Identity. Much research has been done to explain this relation- ship. In the early 1990's, five coding theorists discovered that nonlinear codes have linear properties if viewed under the alphabet Z₄ rather than the usual alphabet F₂. In 1994, these coding theorists published their results in a joint paper in IEEE Transactions on Information Theory. In this study, linear codes and nonlinear codes are introduced and characterized as Z₄-linear codes to understand the importance of this discovery.