R language

Topic 1

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)

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)

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(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

Topic 4 (Question 2)

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.

Concernant le client :
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