Codes over an infinite family of algebras

In this paper, we will show some properties of codes over the ring bk = fp[v1; : : : ; vk]=(v^2i = vi; 8i = 1; : : : ; k): these rings, form a family of commutative algebras over finite field fp. we first discuss about the form of maximal ideals and characterization of automorphisms for the ring bk. then, we define certain gray map which can be used to give a connection between codes over bk and codes over fp. using the previous connection, we give a characterization for equivalence of codes over bk and euclidean self-dual codes. furthermore, we give generators for invariant ring of euclidean self-dual codes over bk through macwilliams relation of hamming weight enumerator for such codes.