Let , be valid generator matrices of dimensions , all over the same field .

        Which of the following are always valid generator matrices? 

        Hint: recall that "valid'' means that for all , and .

with and .

Let , be valid generator matrices of dimensions , all over the same field .

        Which of the following are always valid generator matrices? 

        Hint: recall that "valid'' means that for all , and .

, where and are diagonal matrices with non-zero diagonal elements.

Let , be valid generator matrices of dimensions , all over the same field .

        Which of the following are always valid generator matrices? 

        Hint: recall that "valid'' means that for all , and .

Let , be valid generator matrices of dimensions , all over the same field .

        Which of the following are always valid generator matrices? 

        Hint: recall that "valid'' means that for all , and .

Consider a block code that to a binary sequence associates the codeword , where . This code can detect all the errors of odd weight.

Question 2

Let be a subspace of which consists of elements satisfying,

What is the dimension of ? Check the correct answer.

Question 1

Consider a communication system consisting of a binary block code with codeword uniformly at random chosen, an error channel, and a minimum-distance decoder. Check the correct statement about the minimum-distance decoder.

How many satisfy the equation ?

Question 4c

are valid exponents.