  The codeword stabilized (CWS) quantum codes formalism presents a unifying
approach to both additive and nonadditive quantum error-correcting codes
(arXiv:0708.1021 [quant-ph]), but only for binary states. Here we generalize
the CWS framework to the nonbinary case (of both prime and nonprime dimension)
and map the search for nonbinary quantum codes to a corresponding search
problem for classical nonbinary codes with specific error patterns. We show
that while the additivity properties of nonbinary CWS codes are similar to the
binary case, the structural properties of the nonbinary codes differ
substantially from the binary case, even for prime dimensions. In particular,
we identify specific structure patterns of stabilizer groups, based on which
efficient constructions might be possible for codes that encode more dimensions
than any stabilizer codes of the same length and distance; similar methods
cannot be applied in the binary case. Understanding of these structural
properties can help prune the search space and facilitate the identification of
good nonbinary CWS codes.
