  The existence and uniqueness (up to equivalence) of code loops was first
established by R. Griess. Nevertheless, the explicit construction of code loops
remained open until T. Hsu introduced the notion of symplectic cubic spaces and
their Frattini extensions, and pointed out how the construction of code loops
followed from the (purely combinatorial) result of O. Chein and E. Goodaire.
Within this paper, we focus on their combinatorial construction and prove a
more general result using the language of derived forms.
