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

LP Pseudocodewords of Cycle Codes are Half-Integral