R language

Topic 1 • Task: o Read the page. o Recall that from a generator matrix G in systematic form G = (I|A) we can produce a parity check matrix H = (AT|I). o An alternative standard form for G is G = (A|I). Then a parity-check matrix H is H = (I|AT). o So if G starts with an identity matrix, then H finishes with one. But if G finishes with an identity matrix, then H starts with one. Remember that the identity matrix which is a submatrix of G often has a different order to the identity matrix which is a submatrix of H. Topic 2 (Generator Matrices and the codes they generate) • Task: o Read the commands and try to understand why they produce the output shown. o Fill in the empty box (discussing A as a submatrix of G). o Practise varying the commands in the Code Box and running the code. Topic 3 (Question 1) • Task: o Read and understand the commands in the first code box and click on Run Code. Read and understand the commands in the second code box and click on Run Code. Look at the output, and make sure you understand it. o Question 1(a): Write an answer in the empty box. o Question 1(b): Read and understand the commands in the code box and click on Run Code. Look at the output, and make sure you understand it. o Question 1(c): Read and understand the commands in the code box and click on Run Code. Look at the output, and make sure you understand it. Then write your answer in the empty box. o Question 1(d): Write an answer in the empty box. Then read and understand the commands in the code box and click on Run Code. Look at the output, and make sure you understand it. o Question 1(e): Write your three answers in the empty box. o Question 1(f): Below the empty box, read and understand the commands in the code box and click on Run Code. Look at the output, and make sure you understand it. Then go back up to the empty box and answer the two questions, justifying your answer in each case. Topic 4 (Question 2) • Task: o Read and understand the commands in the first box and the output beneath it. o Question 2(a): Read and understand the instructions, the commands and the output. o Question 2(b): Enter the commands to produce the syndrome of the specified error pattern as a row vector, and the syndromes of the words in the specified coset as a list of 8 row vectors stacked in a matrix. Click on Run Code. Look at the output, and make sure you understand it. o Question 2(c): Click on Run Code. Read and understand the instructions, the commands and the output. o Questions 2(d)--2(g). Omit these, as there’s something wrong with the inbuilt code.