Virtual Labs

1. What is the rank of the parity check matrix of a

\mathbf{(8,5)}

linear code?

a: 4 Explanation

Explanation

b: 5 Explanation

Explanation

c: 3 Explanation

Explanation

d: 7 Explanation

Explanation

2. For an

\mathbf{(n,k)}

code with minimum distance

\mathbf{d}

, what is the maximum number of errors which can be detected?

d

Explanation

d-1

Explanation

\frac{d}{2}

Explanation

\frac{d-1}{2}

Explanation

3. Consider the generator matrix of an

\mathbf{(n,k)}

code over

\mathbb{F}_2

in systematic form given by

\begin{bmatrix} \underbrace{I}_{k \times k} | \underbrace{P}_{k \times (n-k)} \end{bmatrix}

, then what is the partiy check matrix of this code?

\begin{bmatrix} \underbrace{I}_{k \times k} | \underbrace{P}_{k \times (n-k)} \end{bmatrix}

Explanation

\begin{bmatrix} \underbrace{P}_{k \times (n-k)} | \underbrace{I}_{k \times k} \end{bmatrix}

Explanation

\begin{bmatrix} \underbrace{P^t}_{(n-k) \times k} | \underbrace{I}_{(n-k) \times (n-k)} \end{bmatrix}

Explanation

\begin{bmatrix} \underbrace{I}_{(n-k) \times (n-k)} | \underbrace{P^t}_{(n-k) \times k} \end{bmatrix}

Explanation

4. Let

\mathbf{w_{\min}}

denote the minimum Hamming weight of a non-zero codeword in a linear block code

\mathcal{C}

and let

\mathbf{d_{\min}}

denote the minimum distance of the code. Which of the following is true?

w_{\min} = d_{\min}

Explanation

w_{\min} > d_{\min}

Explanation

w_{\min} < d_{\min}

Explanation

d: Varies based on code Explanation

Explanation

5. What is the minimum distance of a single parity check code with block length 7 and dimension 6?

a: 2 Explanation

Explanation

b: 3 Explanation

Explanation

c: 6 Explanation

Explanation

d: 7 Explanation

Explanation

Hamming Codes