The GATE Grind

GATE 2019 EC – Question 17

Communications · Information Theory · 1 mark · Multiple choice

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

  1. 0010011
  2. 1100001
  3. 1111000
  4. 1111111

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Correct answer: (B) 1100001

Explanation

By linearity $c(0010)=c(0011)\oplus c(0001)=1100110\oplus0000111=1100001$.