ABSTRACT
Linear algebra works over any field. Many fruitful code constructions rely on codes defined over a large field and involve “going down” to codes over a small field. Also, there are constructions that work best over larger fields. There is simply no reasonable way to get around linear codes over general finite fields. All the basic facts concerning binary linear codes carry over to general linear codes. The principle of duality, although rather elementary, is very important. One could almost say it distinguishes coding theorists from the rest of the world. In general, the minimum distance of a linear code is far from determining the minimum distance of its dual. The principle of duality relates the minimum distance to a very different parameter of the dual, the strength.
