Does a modulation with q different symbol states absolutely require a
code over X^n, where X = {a_1, a_2, ..., a_q}? Or can you use a
symbol set (X) with a different order (count)?

A slightly different question: is this *typically* done (q symbol states
==> order q symbol set)? I.e., although it's not required, is it
typically done this way?

As a simple example, could a binary (7,4) Hamming code be applied to 16
QAM, such that 4/7 codewords fit into one symbol?
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