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Binary Hamming code

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7. The parity check matrix of a binary [n, k, d] = [15, 11, 3]
Hamming code whose columns are in numeric order is

a) Find the corresponding generator matrix.
Use the method of permuting and unpermuting the columns for the [7, 4, 3]
binary Hamming code.
b) Encode the information vector 10001000001. Explain your steps.
c) What codeword was most likely sent if the received vector is 100010101000000? Explain your steps.
d) What information vector was most likely sent if the received vector is as given in part c? Explain your steps
Note: Assume that the check bits are in columns 1, 2, 4 and 8.

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This answers several questions regarding a binary Hamming code.

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-----62

7. The parity check matrix of a binary [n, k, d] = [15, 11, 3]
Hamming code whose columns are in numeric order is

a) Find the corresponding generator matrix.
Use the method of permuting and unpermuting the columns for the [7, 4, 3]
binary Hamming code.
b) Encode the information vector 10001000001. Explain your steps.
c) What codeword was most likely sent if the received vector is 100010101000000? Explain your steps.
d) What information vector was most likely sent if the received vector is as given in part c? Explain your steps
Note: Assume that the check bits are in columns 1, 2, 4 and 8.

Solution 62
a)
n=15
k=11
d=3
Therefore m=n-k=15-11=4

Generator G= [ Ik (kxk) P (kxm)]

Parity check Matrix H= [ PT Im]

PT = 0 0 0 0 0 0 0 1 1 1 1
0 0 0 1 1 1 1 0 0 0 0
0 1 1 0 0 1 1 0 0 1 1
1 0 1 0 1 0 1 0 1 0 1

Therefore Generator ...

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