We initiate a study of Hamming connected constrained (HCC) codes where any codeword can be transformed into any other by a sequence of single symbol changes such that the intermediate words all satisfy
the constraint. HCC systems might be useful for
encoding data in storage media when a constraint must be met upon writing data,
as might be the case in some emerging storage technologies. The stated property
would permit overwriting encoded data without violating the constraint during
intermediate writes. We study the Hamming connectededness of (d,k) run-length
limited constraints and a few other special cases. We also consider the
decidability of Hamming connectedness for contraints corresponding to walks on
finite labeled graphs.