On semisimple algebra codes: generator theory

The class of affine variety codes is defined as the F-q linear subspaces of A a F-q-semisimple algebra, where F-q is the finite field with q = p(r) elements and characteristic p. It seems natural to impose to the code some extra structure such as been a subalgebra of A. In this case we will have codes that have a Mattson-Solomon transform treatment as the classical cyclic codes. Moreover, the results on the structure of semisimple finite dimen- sional algebras allow us to study those codes from the generator point of view.