The mass formula for self-orthogonal and self-dual codes over a non-unitary commutative ring

In this paper, we establish a mass formula for self-orthogonal codes, quasi self-dual codes, ( ) and self-dual codes over commutative non-unital rings Ip = a, b | pa = pb = 0, a2 = b, ab = 0 , where p is an odd prime. We also give a classification of the three said classes of codes over Ip where p = 3, 5, and 7, with lengths up to 3.