5. Let C be the ternary linear code generated by 1 1 1 1 0 0 0 1 2 0 0 1 0 0 2 2 1 0 00 1 Use Sage to do the following. (Cut and paste your Sage calculations into your homework paper, or print out your calculations) (a) Encode the messages 0102 and 1202. (b) Find a parity check matrix for C (c) Calculate a syndrome lookup table for C (d) Calculate the syndromes of the received words 1221010 and 1020110. (e) Use syndrome decoding to correct the errors in the received words 1221010 and 1020110. 5. Let C be the ternary linear code generated by 1 1 1 1 0 0 0 1 2 0 0 1 0 0 2 2 1 0 00 1 Use Sage to do the following. (Cut and paste your Sage calculations into your homework paper, or print out your calculations) (a) Encode the messages 0102 and 1202. (b) Find a parity check matrix for C (c) Calculate a syndrome lookup table for C (d) Calculate the syndromes of the received words 1221010 and 1020110. (e) Use syndrome decoding to correct the errors in the received words 1221010 and 1020110