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A digital transmission system uses a ($7,4$) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code ($\text{m}_{i}$ ; $\text{c}_{i}$), where $\text{c}_{i}$ is the codeword corresponding to the $i^{th}$ message $\text{m}_{i}$, are known to be $(1100; 0101 100)$, $( 1110; 0011110)$ and $(0110; 1000110)$,  then which of the following is a $\text{valid codeword}$ in this code?

  1. $1101001$
  2. $1011010$
  3. $0001011$
  4. $0110100$
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