  A conceptual framework involving partition functions of normal factor graphs
is introduced, paralleling a similar recent development by Al-Bashabsheh and
Mao. The partition functions of dual normal factor graphs are shown to be a
Fourier transform pair, whether or not the graphs have cycles. The original
normal graph duality theorem follows as a corollary. Within this framework,
MacWilliams identities are found for various local and global weight generating
functions of general group or linear codes on graphs; this generalizes and
provides a concise proof of the MacWilliams identity for linear time-invariant
convolutional codes that was recently found by Gluesing-Luerssen and Schneider.
Further MacWilliams identities are developed for terminated convolutional
codes, particularly for tail-biting codes, similar to those studied recently by
Bocharova, Hug, Johannesson and Kudryashov.
