  The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binary
linear code are defined to be the smallest number of rows in a parity-check
matrix such that the corresponding minimum pseudoweight is equal to the minimum
Hamming distance of the code. It is shown that most codes do not have a finite
pseudocodeword redundancy. Also, upper bounds on the pseudocodeword redundancy
for some families of codes, including codes based on designs, are provided. The
pseudocodeword redundancies for all codes of small length (at most 9) are
computed. Furthermore, comprehensive results are provided on the cases of
cyclic codes of length at most 250 for which the eigenvalue bound of Vontobel
and Koetter is sharp.
