A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111

Q. A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 1100110, then the message 0010 is mapped to

(A) 0010011

(B) 1100001

(C) 1111000

(D) 1111111

Ans: 1100001

Solution:

0010 = (0001) ⊕ → EXOR (0011)

To get the code word, Exor the two code words.

(0000111) ⊕ (1100110)

= 1100001