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A linear Hamming code is used to map $4-bit$ message 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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