In this thesis, we classify all degree p Bethe permanent vectors and Bethe permanent vectors for size 2 x n binary matrices with no zero rows or columns and show that they are pseudocodewords. In doing so, we were able to find a formula for the permanent of the matrix perm [I + P] that is dependent on the size and number of cycles in P, a permutation matrix. We subsequently utilized this result coupled with our novel way to partition Sn, the symmetric group of n elements, to calculate the Bethe permanent of all size 2 x 2 binary matrices
