  Since MacWilliams proved the original identity relating the Hamming weight
enumerator of a linear code to the weight enumerator of its dual code there
have been many different generalizations, leading to the development of
$m$-tuple support enumerators. We prove a generalization of theorems of Britz
and of Ray-Chaudhuri and Siap, which build on earlier work of Kl{\o}ve,
Shiromoto, Wan, and others. We then give illustrations of these $m$-tuple
weight enumerators.
