(a) Find a basis for the Reed-Muller code R(1,3) over F2 = {0,1} and write down all the words of weight 1 in the code. [8] (b) Write down all the words in the Hamming code Ham (2,3) over F3 {0,1,2}. [5] (c) In each of the following cases, give an example of an MDS code of length n and redundancy r over Fq that works for every prime power q. Justify your answer concisely. [3] (i) n = 2020 and r = 1, (ii) n=9+1 and r = 2. (a) Find a basis for the Reed-Muller code R(1,3) over F2 = {0,1} and write down all the words of weight 1 in the code. [8] (b) Write down all the words in the Hamming code Ham (2,3) over F3 {0,1,2}. [5] (c) In each of the following cases, give an example of an MDS code of length n and redundancy r over Fq that works for every prime power q. Justify your answer concisely. [3] (i) n = 2020 and r = 1, (ii) n=9+1 and r = 2