Spectra of phase point operators in odd prime dimensions and the extended Clifford group

We analyze the role of the extended Clifford group in classifying the spectra of phase point operators within the framework laid out by [Gibbons , Phys. Rev. A 70, 062101 (2004)] for setting up Wigner distributions on discrete phase spaces based on finite fields. To do so we regard the set of all the discrete phase spaces as a symplectic vector space over the finite field. Auxiliary results include a derivation of the conjugacy classes of ESL(2,F-N). (c) 2008 American Institute of Physics.