  The Moufang loop named for Richard Parker is a central extension of the
extended binary Golay code. It the prototypical example of a general class of
nonassociative structures known today as code loops, which have been studied
from a number of different algebraic and combinatorial perspectives. This
expository article aims to highlight an experimental approach to computing in
code loops, by a combination of a small amount of precomputed information and
making use of the rich identities that code loops' twisted cocycles satisfy. As
a byproduct we demonstrate that one can reconstruct the multiplication in
Parker's loop from a mere fragment of its twisted cocycle. We also give
relatively large subspaces of the Golay code over which Parker's loop splits as
a direct product.

Combinatorics;Group Theory