coding theory

4. (i) Let C C Z be the 1-error correcting linear code that has parity check matrix (12207 2021 Construct a table listing all the single error syndromes for this code. 3 Marks (b) Using syndrome decoding, what will the receiver con- clude if they receive the word 2222? [2 Marks (c) What will they conclude if the received word is 1220? 2 Marks (d) Are there any circumstances where the receiver would not be able to decode the received word using syndrome decoding? [2 Marks 4. (i) Let C C Z be the 1-error correcting linear code that has parity check matrix (12207 2021 Construct a table listing all the single error syndromes for this code. 3 Marks (b) Using syndrome decoding, what will the receiver con- clude if they receive the word 2222? [2 Marks (c) What will they conclude if the received word is 1220? 2 Marks (d) Are there any circumstances where the receiver would not be able to decode the received word using syndrome decoding? [2 Marks