  Quantum codes are subspaces of the state space of a quantum system that are
used to protect quantum information. Some common classes of quantum codes are
stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained
from stabilizer codes, and Clifford codes. These are analyzed in a framework
using the Fourier transform on finite groups, the finite group in question
being a subgroup of the quantum error group considered. All the classes of
codes that can be obtained in this framework are explored, including codes more
general than Clifford codes. The error detection properties of one of these
more general classes ("direct sums of translates of Clifford codes") are
characterized. Examples codes are constructed, and computer code search results
presented and analysed.
