  We describe a new construction of an incoherent dictionary, referred to as
the oscillator dictionary, which is based on considerations in the
representation theory of finite groups. The oscillator dictionary consists of
order of p^5 unit vectors in a Hilbert space of dimension p, where p is an odd
prime, whose pairwise inner products have magnitude of at most 4/sqrt(p). An
explicit algorithm to construct a large portion of the oscillator dictionary is
presented.
