  In his Ph.D. disseration, Feldman and his collaborators define the linear
programming decoder for binary linear codes, which is a linear programming
relaxation of the maximum-likelihood decoding problem. This decoder does not,
in general, attain maximum-likelihood performance; however, the source of this
discrepancy is known to be the presence of non-integral extreme points
(vertices) within the fundamental polytope, vectors which are also called
nontrivial linear programming pseudocodewords. Restricting to the class of
cycle codes, we provide necessary conditions for a vector to be a linear
programming pseudocodeword. In particular, the components of any such
pseudocodeword can only assume values of zero, one-half, or one.
