Let C be a binary linear code of length n. As usual, we write w(x) for the weight of codeword x, d(x, y) = w(x - y) for the Hamming distance, and d(C) for the minimal distance of the code. Part 1. (10 points) Prove that for any two x, y E C, w(x+y) 2n - w(x) w(y). - Part 2. (10 points) Assume that dimension of C is 2. Prove that d(C) 2n/3. Activate Windows