  We characterize constacyclic codes in the spectral domain using the finite
field Fourier transform (FFFT) and propose a reduced complexity method for the
spectral-domain decoder. Further, we also consider repeated-root constacyclic
codes and characterize them in terms of symmetric and asymmetric $q$-cyclotomic
cosets. Using zero sets of classical self-orthogonal and dual-containing codes,
we derive quantum error correcting codes (QECCs) for both constacyclic
Bose-Chaudhuri-Hocquenghem (BCH) codes and repeated-root constacyclic codes. We
provide some examples of QECCs derived from repeated-root constacyclic codes
and show that constacyclic BCH codes are more efficient than repeated-root
constacyclic codes. Finally, quantum encoders and decoders are also proposed in
the transform domain for Calderbank-Shor-Steane CSS-based quantum codes. Since
constacyclic codes are a generalization of cyclic codes with better minimum
distance than cyclic codes with the same code parameters, the proposed results
are practically useful.
