Say the parity matrix is: [[-1. -1. 0.] [ 0. -2. -2.] [-1. 0. -2.] [ 1. 0. 0.] [ 0. 1. 0.] [ 0. 0. 1.]]
The codewords: c = [[1, 0, 2, 0, 1, 1], [1, 2, 2, 0, 1, 1], [1,1,1,2,0,1]]
And the coding table: (0.0, 0.0, 0.0) (0, 0, 0, 0, 0, 0) (0.0, 0.0, 1.0) (0, 0, 0, 0, 0, 1) (0.0, 0.0, 2.0) (0, 0, 0, 0, 0, 2) (0.0, 1.0, 0.0) (0, 0, 0, 0, 1, 0) (0.0, 1.0, 1.0) (0, 0, 0, 0, 1, 1) (0.0, 1.0, 2.0) (0, 0, 0, 0, 1, 2) (0.0, 2.0, 0.0) (0, 0, 0, 0, 2, 0) (0.0, 2.0, 1.0) (0, 0, 0, 0, 2, 1) (0.0, 2.0, 2.0) (0, 0, 0, 0, 2, 2) (1.0, 0.0, 0.0) (0, 0, 0, 1, 0, 0) (1.0, 0.0, 1.0) (0, 0, 0, 1, 0, 1) (1.0, 0.0, 2.0) (0, 0, 0, 1, 0, 2) (1.0, 1.0, 0.0) (0, 0, 0, 1, 1, 0) (1.0, 1.0, 1.0) (0, 0, 0, 1, 1, 1) (1.0, 1.0, 2.0) (0, 0, 0, 1, 1, 2) (1.0, 2.0, 0.0) (0, 0, 0, 1, 2, 0) (1.0, 2.0, 1.0) (0, 0, 0, 1, 2, 1) (1.0, 2.0, 2.0) (0, 0, 0, 1, 2, 2) (2.0, 0.0, 0.0) (0, 0, 0, 2, 0, 0) (2.0, 0.0, 1.0) (0, 0, 0, 2, 0, 1) (2.0, 0.0, 2.0) (0, 0, 0, 2, 0, 2) (2.0, 1.0, 0.0) (0, 0, 0, 2, 1, 0) (2.0, 1.0, 1.0) (0, 0, 0, 2, 1, 1) (2.0, 1.0, 2.0) (0, 0, 0, 2, 1, 2) (2.0, 2.0, 0.0) (0, 0, 0, 2, 2, 0) (2.0, 2.0, 1.0) (0, 0, 0, 2, 2, 1) (2.0, 2.0, 2.0) (0, 0, 0, 2, 2, 2)
with m = 3, how would you go about decoding c? The answer is [[1, 0, 2], [1, 0, 2], [1, 1, 1]]. I have already looked up plenty of sites but I can't seem to find the solution/algorithm to solving this.
It's a mystery to me how the vectors went from size = 6 to size = 3. Any help is appreciated.