Dat je (n,k)-Linearni kod u 
i kontrolna matrica H, trazi se n,k i skup svih kodova/reci?
![\ H =\left( \begin{array}{ccccc}
0 & 1 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 & 1 \\
1 & 0 & 0 & 1 & 1 \end{array} \right)\]](https://static.elitesecurity.org/tex/a2645bcf6a42339bf88024a5f2f387c5.png)
Prvi put se bavim kodiranjem pa ne znam skoro nista :) .
Znam da mi je potrebna generatorska matrica ( generator matrix ), ali kako ide postupak dobijanja ?
i kontrolna matrica H, trazi se n,k i skup svih kodova/reci?Prvi put se bavim kodiranjem pa ne znam skoro nista :) .
Znam da mi je potrebna generatorska matrica ( generator matrix ), ali kako ide postupak dobijanja ?
![\ H =\left( \begin{array}{ccccc}
0 & 1 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 & 1 \\
1 & 0 & 0 & 1 & 1 \end{array} \right)\] \rightarrow \ H' =\left( \begin{array}{ccccc}
1 & 0 & 0 & 1 & 1 \\
0 & 1 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 & 1 \end{array} \right)\]
\vspace{10 mm}
\ (I_3,A) =\left( \begin{array}{cccccc}
1 & 0 & 0 & |& 1 & 1 \\
0 & 1 & 0 & |& 0 & 1 \\
0 & 0 & 1 & |& 0 & 1 \end{array} \right)\]
\vspace{10 mm}
\ A =\left( \begin{array}{cc}
1 & 1 \\
0 & 1 \\
0 & 1 \end{array} \right)\]
\vspace{10 mm}
\ (-A^{T},I_2) =\left( \begin{array}{cccccc}
1&1 &1& |& 1 & 0 \\
0&0 &1 &|& 0 & 1 \end{array} \right)\]
\vspace{10 mm}
\ G =\left( \begin{array}{cccccc}
1&1 &1& 1 & 0 \\
0&0 &1& 0 & 1 \end{array} \right)\]
\vspace{10 mm}
Dobijem (5,2)-Linearni kod (n=5 i k=2, zbog G matrice), i broj kodova C, q^{k}=2^{2}=4 .
\begin{center} C=\{ 00000, 11110, 00101, 11011 \} \end{center}](https://static.elitesecurity.org/tex/e8c854e82b1fd1be25a321b10fcdfa76.png)
![\left[
\begin{array}{ccc}
2 & 1 & 0
\vspace{0.5em}\\
1 & 2 &3
\end{array}
\right]](https://static.elitesecurity.org/tex/c69000a72855d63d81544e1128f2c5b5.png)
![A =\left[
\begin{array}{ccc}
2 & 1 & 0\\
1 & 2 &3\\
3 & 3& 3
\end{array}
\right]
\vspace{1cm}
A^T=\left[
\begin{array}{ccc}
2 & 1 & 3\\
1 & 2 &3\\
0 & 3& 3
\end{array}
\right]](https://static.elitesecurity.org/tex/ee6e40bb62514d3bd3af0dccb55686fd.png)
