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 .

Note: This is an open question. In the real exam, we will grade your arguments. Here for the quiz, we do not have the capacity to do this. Therefore, you will merely enter your final answer into a multiple choice grid on Moodle. However, do make sure to carefully look at the solution and compare to your answer. How many points would you have given yourself?

Let be a linear block code over of block length such that is even and minimum distance . We construct a new code by appending onto each codeword three parity bits as follows:

,

,

.

The goal is to find the minimum distance of the new linear block code.

Could it happen that , , or

For each case, if it is possible, show how. If it is not possible, argue why not.

Let be a linear block code over with prime and .

Let be a linear block code over of the same dimension . 

Which of the following is true?

Let be a linear code over , and let be a linear code over .

        Answer the following true/false questions.

Let be a linear code over , and let be a linear code over .

        Answer the following true/false questions.

is necessarily a linear code over .

Let 

     be the generator matrix of a linear code over .

        Answer the following true/false questions.

.

Let 

     be the generator matrix of a linear code over .

        Answer the following true/false questions.

Let 

     be the generator matrix of a linear code over .

        Answer the following true/false questions.

Let 

     be the generator matrix of a linear code over .

        Answer the following true/false questions.

admits a systematic form (i.e., it can be put into systematic form via elementary row operations).