sentences:  For example, if a binary code has the generator matrix
  
  then its parity check matrix is
  
  It can be verified that G is a formula_9 matrix, while H is a formula_10 matrix.For any (row) vector x of the ambient vector space, s = "H"x⊤ is called the syndrome of x.The vector x is a codeword if and only if s = 0.