Example 12.Suppose that we have the following eight words to be encoded: (000),(001),(010),..,(111) For the associated standard generator and canonical parity-check matrices are 0 01 0 1110 0 0 Codeword 1 001 G 0 0 Gx 0100 0 1 0 000000 1 0 001101 010110 If x =(x1,22,23,24,25,6),then 011011 100011 x2+x3+x4 101110 0=Hx= 1+2十5 恰好是H的 110101 1+T3+6 null space! 111000恰好是H的 null space!