Media type: E-Article Title: The input–output weight enumeration of binary Hamming codes Contributor: Loskot, Pavel; Beaulieu, Norman C. imprint: Wiley, 2006 Published in: European Transactions on Telecommunications Language: English DOI: 10.1002/ett.1133 ISSN: 1124-318X; 1541-8251 Keywords: Electrical and Electronic Engineering Origination: Footnote: Description: <jats:title>Abstract</jats:title><jats:p>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 © 2006 AEIT</jats:p>