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 $ {{\mathit {I}_p}} = \left < a, b | pa = pb = 0, a^2 = b, ab = 0 \right > $, where $ p $ is an odd prime. We also give a classification of the three said classes of codes over $ {{\mathit {I}_p}} $ where $ p = 3, 5, $ and $ 7 $, with lengths up to $ 3 $.