  We analyse some features of the class of discrete Wigner functions that was
recently introduced by Gibbons et al. to represent quantum states of systems
with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101
(2004)]. We consider "cat" states obtained as coherent superpositions of states
with positive Wigner function; for such states we show that the oscillations of
the discrete Wigner function typically spread over the entire discrete
phase-space (including the regions where the two interfering states are
localized). This is a generic property which is in sharp contrast with the
usual attributes of Wigner functions that make them useful candidates to
display the existence of quantum coherence through oscillations. However, it is
possible to find subsets of cat states with a natural phase-space
representation, in which the oscillatory regions remain localized. We show that
this can be done for interesting families of stabilizer states used in quantum
error-correcting codes, and illustrate this by analysing the phase-space
representation of the five-qubit error-correcting code.
