title: Hamming codes formulas
body: <p>This is the question: </p>
  
  <p><em>Determine if the Hamming codes (15,10), (14,10) and (13,10) can correct a single error (SEC), detect a single error (SED) or detect double bit errors (DED).</em> </p>
  
  <p>I do know how Hamming distance work and how you can detect an error if you have the data-word that you want to transmit. But I don't know how to do it without the data-word.</p>
  
  <p>Only for SEC which has the formula:</p>
  
  <p>2^m > m+k+1</p>
  
  <p>where</p>
  
  <p>m = check bits
  k = data bits</p>
  
  <p>But is the any formulas for SED and DED? I have searched google all day long without any success. </p>