Let <i>C</i> be an (<I>n,k</i>) linear code over <I>F</i> with generator matrix <I>G</i> and parity-check matrix <I>H</i>.  Then, for any vector <I>v</i> in <i>F<sup>n</sup></i>,
we have <i>vH = 0</i>  (the zero vector) if any only if <I>v</i> belongs to <I>C</i>.