Define a family of matrices inductively as follows: G 0 = [1] and, for n ¥ 1,
Question:
G0= [1] and, for n ¥ 1,
where 0 is a zero vector and 1 is a vector consisting entirely of ones.
(a) Write out G1, G2, and G3.
(b) Using induction, prove that for all n ¥ 0, Gn is a generator matrix for the Reed-Muller code Rn.
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