Question: Messages are being transmitted by an error - correcting Hamming ( 7 , 4 ) code with generator matrix G = 1 0 0 0

Messages are being transmitted by an error

-

correcting Hamming

(7, 4)

code with generator matrix

G

=

1 0 0 0 1 1 0

0 1 0 0 1 0 1

0 0 1 0 0 1 1

0 0 0 1 1 1 1

and you receive the following transmissions:

c

1 = (1, 0, 0, 1, 0, 1, 0),

c

2 = (1, 1, 1, 1, 0, 0, 1)

and c

3 = (1, 0, 1, 0, 0, 1, 0) .

Which of these are legitimate codewords?

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