sentences:  That is, they show how linear combinations of certain digits (components) of each codeword equal zero.For example, the parity check matrix
  
  compactly represents the parity check equations,
  that must be satisfied for the vector formula_3 to be a codeword of "C".From the definition of the parity-check matrix it directly follows the minimum distance of the code is the minimum number "d" such that every "d - 1" columns of a parity-check matrix "H" are linearly independent while there exist "d" columns of "H" that are linearly dependent.