Ergodic theory over F2〚T〛

In cryptography and coding theory, it is important to study the pseudo-random sequences and the ergodic transformations. We already have the ergodic 1-Lipschitz theory over Z2 established by V. Anashin and others. In this paper we present an ergodic theory over F2〚T〛 and some ideas which might be very useful in applications.