  In 1962, Jesse MacWilliams published a set of formulas for linear and abelian
group codes that among other applications, were incredibly valuable in the
study of self-dual codes. Now called the MacWilliams Identities, her results
relate the weight enumerator and complete weight enumerator of a code to those
of its dual code. A similar set of MacWilliams identities has been proven to
exist for many other types of codes. In 2013, Dougherty, Sol\'{e}, and Kim
published a list of fundamental open questions in coding theory. Among them,
Open Question 4.3: "Is there a duality and MacWilliams formula for codes over
non-Abelian groups?" In this paper, we propose a duality for nonabelian group
codes in terms of the irreducible representations of the group. We show that
there is a Greene's Theorem and MacWilliams Identities which hold for this
notion of duality. When the group is abelian, our results are equivalent to
existing formulas in the literature.
