Problem 11 Suppose that Alice meant to send the vector Gbig. However, the first bit of her message got flipped, so Bob received y instead. What will Hbigy be? What would Hbigy be if the ninth bit had been flipped instead? Alice encodes her message, which is 50 characters long, into 5 bit vectors in the following manner: space 00000 A 00001 B 00010 C 00011 Z 11010 She then encodes these vectors with Gbig, making them 9 bits long, and sends them to Bob. The message Bob receives is on the next page, and can be downloaded from http://www.math. Isa. umich . edu/courses/214/project_files/message. csv. Each vector is either the one Alice sent, or else differs from what she sent by a single bit flip.A matrix H with kernel V is called a parity check matrix. Applying any row operation to H will not change the kernel, so the parity check matrix is not unique. A larger code. We now consider a code with N = 32, p = 2 and n = 9. This code has generator matrix and parity check matrix: 10000 01000 33333 110011000 111000100 Gb1g=00001 Hb13=101100010 11001 11100 100110001 10110 10011