THE NUMBER OF CODES OVER RINGS OF ORDER 4 CONTAINING A HULL OF GIVEN TYPE

We study the hull, that is the intersection of a code with its orthogonal, of both linear and additive codes over the rings with unity of order 4, where the orthogonal is the Euclidean orthogonal for linear codes and for additive codes it is determined using characters. We relate the hull of the code with the hull of its image under the corresponding Gray map and use this to count the number of codes with a given hull for additive codes for the rings with characteristic 2. We investigate the codes over these rings which have a hull of given type which gives the cardinality of the hull.