Problem
In the course material, error correcting encoding and decoding is described through a Hamming code. There are many other codes defifined over the years. The one treated in this problem is called Reed-Muller code.
For a positive integer m and a non-negative integer r, the generator matrix for the ReedMuller code RM(r, m) is defifined as
G(r, m) = G(r, m 1)G(r,m 1)0G(r 1,m 1)
To start the induction, defifine G(0, m) as a row vector of 2m ones, i.e. the generator matrix for a length 2m repetition code, and G(m, m) the unit matrix of size 2m. In this problem the RM(1, 3) code will be treated.
