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Aim

Theory

Pretest

Procedure

Simulation

Posttest

References

Contributors

Feedback

Hamming Codes

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Beginner

Intermediate

Advanced

1. The number of codewords in a

\mathbf{(7,4,3)}

Hamming code is

a: 4 Explanation

Explanation

b: 8 Explanation

Explanation

c: 16 Explanation

Explanation

d: 32 Explanation

Explanation

2. Which of the following is a codeword of the Hamming code?

\begin{bmatrix} 1 & 0 & 1 & 1 & 0 & 1 & 1 \end{bmatrix}

Explanation

\begin{bmatrix} 0 & 0 & 1 & 1 & 1 & 0 & 1 \end{bmatrix}

Explanation

\begin{bmatrix} 1 & 0 & 0 & 1 & 0 & 0 & 1 \end{bmatrix}

Explanation

\begin{bmatrix} 0 & 1 & 0 & 1 & 1 & 1 & 0 \end{bmatrix}

Explanation

3. What is the number of vectors which are at a Hamming distance

\mathbf{1}

from a given codeword in the Hamming code?

a: 4 Explanation

Explanation

b: 5 Explanation

Explanation

c: 7 Explanation

Explanation

d: 9 Explanation

Explanation

4. If Hamming code is used as an error-detecting code, how many errors can a Hamming code detect?

a: 1 Explanation

Explanation

b: 2 Explanation

Explanation

c: 3 Explanation

Explanation

d: 4 Explanation

Explanation

5. What is the minimum distance of the dual of

\mathbf{(7,4,3)}

Hamming code?

a: 4 Explanation

Explanation

b: 3 Explanation

Explanation

c: 5 Explanation

Explanation

d: 6 Explanation

Explanation

6. Consider an extended Hamming code of length

\mathbf{8}

and dimension

\mathbf{4}

obtained by adding a partiy bit to the codeword of the Hamming code based on the following equation:

\begin{equation*} p_8 = \sum_{i=1}^4 m_i + \sum_{i=5}^7 p_i \end{equation*}

Thus, the codeword of the extended Hamming code is given by

\mathbf{[m_1, m_2, m_3, m_4, p_5, p_6, p_7, p_8]}

. What is the minimum distance of the extended Hamming code?

a: 3 Explanation

Explanation

b: 5 Explanation

Explanation

c: 4 Explanation

Explanation

d: 6 Explanation

Explanation

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