In GF(23) finite field, for the irreducible polynomial p(x)=x3 +x2 +1 and primitive element is a , find the answers for [7,3] Reed-Solomon code a) Find the generator poly finite field nomial b) Find the Generator Matrix and put it into standard form. c) Code the message m =(102 a) d) Received message is f(x)= a x2 + ax3 Find the syndrome polynomial S (x) for decode the received message. e) Fill in the table by performing the necessary division operations using the Euclidean algorithm. "; = 'i-2-9;!;(remainder) 9, (quotient)t; = 1;-2 - 9;ti-1 -1 0 X-k = X2 S(X) = ? 0 1 1 ...? ..? ...? 2 W (x) = ? ? 0,(x) = ? f) Find the errors from the error location polynomial ( 0,(x) ) Wa") g) Find the error values by using o'(a) for ji. h) What is an error polynomial and a decoding polynomial