The Hamming code. For example, take N = 8, p = 2, n = 7, Alice could choose the following N codewords to represent the messages she might send: Code Word Message 0000000 Hello 1001101 Goodbye. 0101011The water is fine. 1100110I have met an unusual animal. 1011010 I just saw a rainbow. 0111100 I'm ready to return. 1110001 Send help immediately! A code is called linear when the list of code words is a linear subspace of Fp. Let VHamming be the list of codewords above Problem 4 Give a basis of VHamming, and give a matrix GHamming whose image is VHamming The Hamming code. For example, take N = 8, p = 2, n = 7, Alice could choose the following N codewords to represent the messages she might send: Code Word Message 0000000 Hello 1001101 Goodbye. 0101011The water is fine. 1100110I have met an unusual animal. 1011010 I just saw a rainbow. 0111100 I'm ready to return. 1110001 Send help immediately! A code is called linear when the list of code words is a linear subspace of Fp. Let VHamming be the list of codewords above Problem 4 Give a basis of VHamming, and give a matrix GHamming whose image is VHamming