The input-output weight enumeration of binary Hamming codes

We show that binary Hamming codes can be constructed recursively. The recursive structure is used to efficiently enumerate the input-output weights. Hence, the bit error rate of binary Hamming codes with antipodal signalling and hard-decision demodulation used on additive white Gaussian noise channels can be evaluated exactly. The numerically computed coding gain of Hamming codes reveals a surprising fact that the coding gain is not monotonically increasing with signal-to-noise ratio. Copyright (C) 2006 AEIT.