Self-dual codes over

The focus in this work is on self-dual codes over the ring F 2 + u F 2 + v F 2 + uv F 2 . Type I and Type II codes over F 2 + u F 2 + v F 2 + uv F 2 are defined and some of the techniques used in the literature are applied to get some theoretical results about self-dual codes on F 2 + u F 2 + v F 2 + uv F 2 and their binary images. In particular some extremal and optimal binary codes of Type I and Type II including the extended Golay code are obtained as the Gray images of codes over F 2 + u F 2 + v F 2 + uv F 2 .