The following is a generating matrix for a group code: G= 1 0 0 0 0...

  

Transcribed Image Text:

The following is a generating matrix for a group code: G= 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 (a) Use it to encode the following two messages: (1011) and (0110). (b) Write out the parity check matrix H associated with G. (c) Using H, correct (when necessary) the following two received words, assuming at most one bit is in error (or else explain why you think that cannot be done): (i) r = (1000 011), and (ii) s = = (1110 001). (d) Write down the original message words for each of the received words in part (c). The following is a generating matrix for a group code: G= 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 (a) Use it to encode the following two messages: (1011) and (0110). (b) Write out the parity check matrix H associated with G. (c) Using H, correct (when necessary) the following two received words, assuming at most one bit is in error (or else explain why you think that cannot be done): (i) r = (1000 011), and (ii) s = = (1110 001). (d) Write down the original message words for each of the received words in part (c).