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DefinitionEdit

Given two squences (or strings) of symbols in an alphabet $ \mathcal{L} $, the Hamming similarity is a function $ HammingSim:\mathcal{L}^*\times\mathcal{L}^*\longrightarrow [0,1] $ that measures the number of positions for which the corresponding symbols are equals, divided by the length of the bigest sequence:

$ HammingSim(s,t)=\frac{\sum_{i=1}^{\min\{|s|,|t|\}}IdSim(s[i],t[i])}{\max\{|s|,|t|\}}, $

where $ IdSim $ is the Identity similarity.

Examples Edit

  • HammingSim('house','horse') = 4/5 = 0.8.
  • HammingSim('abcd',' ') = 0/4 = 0.
  • HammingSim('abcd','a') = 1/4 = 0.25.
  • HammingSim('abcd','b') = 0/4 = 0.
  • HammingSim('id0345','id1352') = 3/6 = 0.5.

Normalization Edit

It is normalized.

Applications Edit

  • Comparing codes.

References Edit