= {00000001, 12121001, 21212000, 11001222}. Find 2. (a) Consider the ternary code C the greatest number of errors that C can correct. [6 marks] (b) Suppose C is a linear code and suppose d(C) is odd. Suppose ec is the greatest number of errors that C can correct and sc is the greatest number of errors that C can detect. Then, prove that 1+(ec + sc) = wt(C) [10 marks] (c) Prove that there is no ternary code C with |C|= 16 such that C has length 8 and [8 marks] corrects 3 errors. (d) Is there a binary code C with |C| = 12 such that C has length 15 and corrects 2 errors? Justify your answer. 19 marks