Cyclic additive codes and cyclic quantum stabilizer codes

The theory of cyclic linear codes in its ring-theoretic formulation is a core topic of classical coding theory. A simplified approach is in my textbook [1]. The language of ring theory is not needed. We will present a self-contained description of the more general theory of cyclic additive codes using the same method. This includes cyclic quantum stabilizer codes as a special case. The basic ingredients needed are finite field extensions, their Galois groups, the trace, cyclotomic cosets, Lagrange interpolation and bilinear forms, not more. This is based on the paper [2].