Stopping set analysis for Hamming codes

In the 2004 Shannon Lecture, McEliece presented an expression for the number of stopping sets of size three in a Hamming code. In this paper, we investigate how this number depends on the parity-check matrix used in the decoding process. First, we present basic results on stopping set enumerators for block codes in general. Next, we focus on stopping set enumerators for Hamming codes. Our main result is a parity-check matrix of relatively small size for which the number of stopping sets of size three equals the number of codewords of weight three in the Hamming code.