  Error-correcting codes have an important role in data storage and
transmission and in cryptography, particularly in the post-quantum era.
Hermitian matrices over finite fields and equipped with the rank metric have
the potential to offer enhanced security with greater efficiency in encryption
and decryption. One crucial tool for evaluating the error-correcting
capabilities of a code is its weight distribution and the MacWilliams Theorem
has long been used to identify this structure of new codes from their known
duals. Earlier papers have developed the MacWilliams Theorem for certain
classes of matrices in the form of a functional transformation, developed using
$q$-algebra, character theory and Generalised Krawtchouk polynomials, which is
easy to apply and also allows for moments of the weight distribution to be
found. In this paper, recent work by Kai-Uwe Schmidt on the properties of codes
based on Hermitian matrices such as bounds on their size and the eigenvalues of
their association scheme is extended by introducing a negative-$q$ algebra to
establish a MacWilliams Theorem in this form together with some of its
associated moments. The similarities in this approach and in the paper for the
Skew-Rank metric by Friedlander et al. have been emphasised to facilitate
future generalisation to any translation scheme.
