CS 70Discrete Mathematics and Probability TheorySpring 2020Course NotesMT2 Review1List Decoding(a) Consider anncharacter message encoded intomcharacters over the field GF(p)using poly-nomials. Suppose that one receivesn-1 of thempackets. Give a method to find a list of sizeat mostpof all possible messages.(b) Consider anncharacter message encoded intom=n+2kcharacters over the field GF(p)using polynomials. Suppose thatk+1 of themreceived packets are corrupted. Find a list ofall possible messages which contain the original message. What is the size of the list?(c) Consider the protocol in (b) where we are working in GF(7). Let the original message haven=1 andk=2, so there are 5 symbols. Now suppose that there are 3 errors, but these threeerrors all landed on different values. Assume that we received: 0,0,1,2,3. How does yourlist-decoding strategy perform?2Binomial TheoremImagine you are throwingnnumbered balls into bins. There arexred bins andyblue bins.