Ex11 1

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\mathbf{Exercise\ 11.1}$\label{313Code}

For the code $C: \mathbf{Z}_2^1 \to \mathbf{Z}_2^3$ defined by generator matrix

(1)
\begin{align} G=\left(\begin{array}{c}1\\1\\1\end{array}\right) \end{align}

give

  • the set of code words
  • two distinct parity check matrices
(2)
\begin{align} P = \left(\begin{array}{ccc}1&0&1\\0&1&1\end{array}\right). \end{align}
(3)
\begin{align} P = \left(\begin{array}{ccc}1&1&0\\1&0&1\end{array}\right). \end{align}
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