[10+(10+5+5+5)=35 marks ] (a) The binary string f=10111000 is a codeword in the Reed-Muller code RM(3,2). Find the corresponding Boolean function f=f(x1,x2,x3) as a sum of monomials of degree 2 (b) On the attachment page is a table for the Reed-Muller code RM(3,1). A codeword c is converted to a signal s by means of the usual mapping, as displayed in the table. Subsequently the signal s becomes distorted during transmission. The word r=(0.5,1,1,2,1,0,1,1) is received. (i) Compute H8rT using either matrix multiplication or the fast Hadamard transform. (ii) Use your result to find the correct signal. (iii) Then use the table to identify the original codeword and the corresponding message word. (iv) Assuming the original codeword is retrieved, how many errors were corrected