Question

Let $H = \begin{bmatrix} 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ \end{bmatrix}$ be the parity-check matrix for $Ham(3, 2)$, that is, the Hamming code with $q = 2$ and $r = 3$. Which of the following sets contains only codewords? Explain. A = {1010101, 1100110, 1110101} B = {0110011, 1111111, 0110111} C = {1110000, 1110011, 1100110} D = {0010110, 0001111, 1010101}

          Let $H = \begin{bmatrix} 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ \end{bmatrix}$ be the parity-check matrix for $Ham(3, 2)$, that is, the Hamming code with $q = 2$ and $r = 3$. Which of the following sets contains only codewords? Explain.

A = {1010101, 1100110, 1110101}
B = {0110011, 1111111, 0110111}
C = {1110000, 1110011, 1100110}
D = {0010110, 0001111, 1010101}

Let H =
< b m a t r i x > be the parity-check matrix for Ham(3, 2), that is, the Hamming code with q = 2 and r = 3. Which of the following sets contains only codewords? Explain.

A = 1010101, 1100110, 1110101
B = 0110011, 1111111, 0110111
C = 1110000, 1110011, 1100110
D = 0010110, 0001111, 1010101

Added by Y?N O.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Christopher Dzorkpata

07/14/2021

Step 1

To do this, we need to check if the parity-check matrix H multiplied by each codeword in the set results in the zero vector. Show more…

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Let H 0 0 0 be the parity-check matrix for Ham(3,2), that is, the Hamming code with q = 2 and r = 3. Which of the following sets contains only codewords? Explain. A={1010101, 1100110,1110101} B={0110011,1111111,0110111} C={1110000,1110011,1100110} D={0010110,0001111,1010101}