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The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binarylinear code are defined to be the smallest number of rows in a parity-checkmatrix such that the corresponding minimum pseudoweight is equal to the minimumHamming distance of the code. It is shown that most codes do not have a finitepseudocodeword redundancy. Also, upper bounds on the pseudocodeword redundancyfor some families of codes, including codes based on designs, are provided. Thepseudocodeword redundancies for all codes of small length (at most 9) arecomputed. Furthermore, comprehensive results are provided on the cases ofcyclic codes of length at most 250 for which the eigenvalue bound of Vontobeland Koetter is sharp.

On the Pseudocodeword Redundancy of Binary Linear Codes