LAUSR

There is a special local ring E of order 4, without identity for the multiplication, defined by E = a, b | 2a = 2b = 0, a 2 = a, b 2 = b, ab = a, ba = b. We study the algebraic structure of linear codes over that non-commutative local ring, in particular their residue and torsion codes. We introduce the notion of quasi self-dual codes over E, and Type IV codes, that is quasi self-dual codes whose all codewords have even Hamming weight. We study the weight enumerators of these codes by means of invariant theory, and classify them in short lengths.