hilfstabellen updated

3 files changed, 343 insertions, 41 deletions

diff --git a/buch/papers/reedsolomon/hilfstabellen.tex b/buch/papers/reedsolomon/hilfstabellen.tex
index 10e4fd1..4e39de5 100644
--- a/buch/papers/reedsolomon/hilfstabellen.tex
+++ b/buch/papers/reedsolomon/hilfstabellen.tex
@@ -8,8 +8,6 @@
 	\label{reedsolomon:section:hilfstabellen}}
 \rhead{Hilfstabellen}
 
-\textbf{TODO}: gibt es eine besser darstellungsart der tabellen? (\& platzierung der subsections)
-
 Um das rechnen  zu erleichtern findet man in diesem Abschnitt die Resultate, die bei der Addition und der Multiplikation in $\mathbb{F}_{11}$ resultieren.
 
 \subsection{Additionstabelle
diff --git a/buch/papers/reedsolomon/restetabelle1.tex b/buch/papers/reedsolomon/restetabelle1.tex
index a5055c0..3969ef2 100644
--- a/buch/papers/reedsolomon/restetabelle1.tex
+++ b/buch/papers/reedsolomon/restetabelle1.tex
@@ -1,24 +1,176 @@
 % created by Michael Steiner
 %
 % Restetabelle von F_11: Addition
-\begin{figure}
+
+% alternatives design
+%\begin{figure}
+%\begin{center}
+%\begin{tabular}{|>{$}c<{$}|>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}|}
+%\hline
+%+&0&1&2&3&4&5&6&7&8&9&10\\
+%\hline
+%0&0&1&2&3&4&5&6&7&8&9&10\\
+%1&1&2&3&4&5&6&7&8&9&10&0\\
+%2&2&3&4&5&6&7&8&9&10&0&1\\
+%3&3&4&5&6&7&8&9&10&0&1&2\\
+%4&4&5&6&7&8&9&10&0&1&2&3\\
+%5&5&6&7&8&9&10&0&1&2&3&4\\
+%6&6&7&8&9&10&0&1&2&3&4&5\\
+%7&7&8&9&10&0&1&2&3&4&5&6\\
+%8&8&9&10&0&1&2&3&4&5&6&7\\
+%9&9&10&0&1&2&3&4&5&6&7&8\\
+%10&10&0&1&2&3&4&5&6&7&8&9\\
+%\hline
+%\end{tabular}
+%\end{center}
+%\end{figure}
+
 \begin{center}
-\begin{tabular}{|>{$}c<{$}|>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}|}
-\hline
-+&0&1&2&3&4&5&6&7&8&9&10\\
-\hline
-0&0&1&2&3&4&5&6&7&8&9&10\\
-1&1&2&3&4&5&6&7&8&9&10&0\\
-2&2&3&4&5&6&7&8&9&10&0&1\\
-3&3&4&5&6&7&8&9&10&0&1&2\\
-4&4&5&6&7&8&9&10&0&1&2&3\\
-5&5&6&7&8&9&10&0&1&2&3&4\\
-6&6&7&8&9&10&0&1&2&3&4&5\\
-7&7&8&9&10&0&1&2&3&4&5&6\\
-8&8&9&10&0&1&2&3&4&5&6&7\\
-9&9&10&0&1&2&3&4&5&6&7&8\\
-10&10&0&1&2&3&4&5&6&7&8&9\\
-\hline
-\end{tabular}
+
+\begin{tikzpicture}[>=latex,thick,scale=0.45]
+\fill[color=gray!40] (0,0) rectangle (18,-1.5);
+\fill[color=gray!40] (0,0) rectangle (1.5,-18);	
+\draw[step = 1.5, gray,very thin] (0,0) grid (18,-18);
+\draw[very thick] (0,0) rectangle (18,-18);
+\draw[very thick] (0,-1.5) -- (18,-1.5);
+\draw[very thick] (1.5,0) -- (1.5,-18);
+\node at (0.75,-0.75) {$+$};
+\foreach \x in {0,...,10}
+	\node at (2.25+\x*1.5,-0.75) {$\x$};
+\foreach \y in {0,...,10}
+	\node at (0.75,-2.25+\y*-1.5) {$\y$};
+% Row 0
+\node at ( 2.25,-2.25) {$0$};
+\node at ( 3.75,-2.25) {$1$};
+\node at ( 5.25,-2.25) {$2$};
+\node at ( 6.75,-2.25) {$3$};
+\node at ( 8.25,-2.25) {$4$};
+\node at ( 9.75,-2.25) {$5$};
+\node at (11.25,-2.25) {$6$};
+\node at (12.75,-2.25) {$7$};
+\node at (14.25,-2.25) {$8$};
+\node at (15.75,-2.25) {$9$};
+\node at (17.25,-2.25) {$10$};
+% Row 1
+\node at ( 2.25,-3.75) {$1$};
+\node at ( 3.75,-3.75) {$2$};
+\node at ( 5.25,-3.75) {$3$};
+\node at ( 6.75,-3.75) {$4$};
+\node at ( 8.25,-3.75) {$5$};
+\node at ( 9.75,-3.75) {$6$};
+\node at (11.25,-3.75) {$7$};
+\node at (12.75,-3.75) {$8$};
+\node at (14.25,-3.75) {$9$};
+\node at (15.75,-3.75) {$10$};
+\node at (17.25,-3.75) {$0$};
+% Row 2
+\node at ( 2.25,-5.25) {$2$};
+\node at ( 3.75,-5.25) {$3$};
+\node at ( 5.25,-5.25) {$4$};
+\node at ( 6.75,-5.25) {$5$};
+\node at ( 8.25,-5.25) {$6$};
+\node at ( 9.75,-5.25) {$7$};
+\node at (11.25,-5.25) {$8$};
+\node at (12.75,-5.25) {$9$};
+\node at (14.25,-5.25) {$10$};
+\node at (15.75,-5.25) {$0$};
+\node at (17.25,-5.25) {$1$};
+% Row 3
+\node at ( 2.25,-6.75) {$3$};
+\node at ( 3.75,-6.75) {$4$};
+\node at ( 5.25,-6.75) {$5$};
+\node at ( 6.75,-6.75) {$6$};
+\node at ( 8.25,-6.75) {$7$};
+\node at ( 9.75,-6.75) {$8$};
+\node at (11.25,-6.75) {$9$};
+\node at (12.75,-6.75) {$10$};
+\node at (14.25,-6.75) {$0$};
+\node at (15.75,-6.75) {$1$};
+\node at (17.25,-6.75) {$2$};
+% Row 4
+\node at ( 2.25,-8.25) {$4$};
+\node at ( 3.75,-8.25) {$5$};
+\node at ( 5.25,-8.25) {$6$};
+\node at ( 6.75,-8.25) {$7$};
+\node at ( 8.25,-8.25) {$8$};
+\node at ( 9.75,-8.25) {$9$};
+\node at (11.25,-8.25) {$10$};
+\node at (12.75,-8.25) {$0$};
+\node at (14.25,-8.25) {$1$};
+\node at (15.75,-8.25) {$2$};
+\node at (17.25,-8.25) {$3$};
+% Row 5
+\node at ( 2.25,-9.75) {$5$};
+\node at ( 3.75,-9.75) {$6$};
+\node at ( 5.25,-9.75) {$7$};
+\node at ( 6.75,-9.75) {$8$};
+\node at ( 8.25,-9.75) {$9$};
+\node at ( 9.75,-9.75) {$10$};
+\node at (11.25,-9.75) {$0$};
+\node at (12.75,-9.75) {$1$};
+\node at (14.25,-9.75) {$2$};
+\node at (15.75,-9.75) {$3$};
+\node at (17.25,-9.75) {$4$};
+% Row 6
+\node at ( 2.25,-11.25) {$6$};
+\node at ( 3.75,-11.25) {$7$};
+\node at ( 5.25,-11.25) {$8$};
+\node at ( 6.75,-11.25) {$9$};
+\node at ( 8.25,-11.25) {$10$};
+\node at ( 9.75,-11.25) {$0$};
+\node at (11.25,-11.25) {$1$};
+\node at (12.75,-11.25) {$2$};
+\node at (14.25,-11.25) {$3$};
+\node at (15.75,-11.25) {$4$};
+\node at (17.25,-11.25) {$5$};
+% Row 7
+\node at ( 2.25,-12.75) {$7$};
+\node at ( 3.75,-12.75) {$8$};
+\node at ( 5.25,-12.75) {$9$};
+\node at ( 6.75,-12.75) {$10$};
+\node at ( 8.25,-12.75) {$0$};
+\node at ( 9.75,-12.75) {$1$};
+\node at (11.25,-12.75) {$2$};
+\node at (12.75,-12.75) {$3$};
+\node at (14.25,-12.75) {$4$};
+\node at (15.75,-12.75) {$5$};
+\node at (17.25,-12.75) {$6$};
+% Row 8
+\node at ( 2.25,-14.25) {$8$};
+\node at ( 3.75,-14.25) {$9$};
+\node at ( 5.25,-14.25) {$10$};
+\node at ( 6.75,-14.25) {$0$};
+\node at ( 8.25,-14.25) {$1$};
+\node at ( 9.75,-14.25) {$2$};
+\node at (11.25,-14.25) {$3$};
+\node at (12.75,-14.25) {$4$};
+\node at (14.25,-14.25) {$5$};
+\node at (15.75,-14.25) {$6$};
+\node at (17.25,-14.25) {$7$};
+% Row 9
+\node at ( 2.25,-15.75) {$9$};
+\node at ( 3.75,-15.75) {$10$};
+\node at ( 5.25,-15.75) {$0$};
+\node at ( 6.75,-15.75) {$1$};
+\node at ( 8.25,-15.75) {$2$};
+\node at ( 9.75,-15.75) {$3$};
+\node at (11.25,-15.75) {$4$};
+\node at (12.75,-15.75) {$5$};
+\node at (14.25,-15.75) {$6$};
+\node at (15.75,-15.75) {$7$};
+\node at (17.25,-15.75) {$8$};
+% Row 10
+\node at ( 2.25,-17.25) {$10$};
+\node at ( 3.75,-17.25) {$0$};
+\node at ( 5.25,-17.25) {$1$};
+\node at ( 6.75,-17.25) {$2$};
+\node at ( 8.25,-17.25) {$3$};
+\node at ( 9.75,-17.25) {$4$};
+\node at (11.25,-17.25) {$5$};
+\node at (12.75,-17.25) {$6$};
+\node at (14.25,-17.25) {$7$};
+\node at (15.75,-17.25) {$8$};
+\node at (17.25,-17.25) {$9$};
+\end{tikzpicture}
+
 \end{center}
-\end{figure}
\ No newline at end of file
diff --git a/buch/papers/reedsolomon/restetabelle2.tex b/buch/papers/reedsolomon/restetabelle2.tex
index 887c981..1a9815c 100644
--- a/buch/papers/reedsolomon/restetabelle2.tex
+++ b/buch/papers/reedsolomon/restetabelle2.tex
@@ -1,24 +1,176 @@
 % created by Michael Steiner
 %
 % Restetabelle von F_11: Multiplikation
-\begin{figure}
+
+% alternatives design
+%\begin{figure}
+%\begin{center}
+%\begin{tabular}{|>{$}c<{$}|>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}|}
+%\hline
+%\cdot&0&1&2&3&4&5&6&7&8&9&10\\
+%\hline
+%0&0&0&0&0&0&0&0&0&0&0&0\\
+%1&0&1&2&3&4&5&6&7&8&9&10\\
+%2&0&2&4&6&8&10&1&3&5&7&9\\
+%3&0&3&6&9&1&4&7&10&2&5&8\\
+%4&0&4&8&1&5&9&2&6&10&3&7\\
+%5&0&5&10&4&9&3&8&2&7&1&6\\
+%6&0&6&1&7&2&8&3&9&4&10&5\\
+%7&0&7&3&10&6&2&9&5&1&8&4\\
+%8&0&8&5&2&10&7&4&1&9&6&3\\
+%9&0&9&7&5&3&1&10&8&6&4&2\\
+%10&0&10&9&8&7&6&5&4&3&2&1\\
+%\hline
+%\end{tabular}
+%\end{center}
+%\end{figure}
+
 \begin{center}
-\begin{tabular}{|>{$}c<{$}|>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}>{$}c<{$}|}
-\hline
-\cdot&0&1&2&3&4&5&6&7&8&9&10\\
-\hline
-0&0&0&0&0&0&0&0&0&0&0&0\\
-1&0&1&2&3&4&5&6&7&8&9&10\\
-2&0&2&4&6&8&10&1&3&5&7&9\\
-3&0&3&6&9&1&4&7&10&2&5&8\\
-4&0&4&8&1&5&9&2&6&10&3&7\\
-5&0&5&10&4&9&3&8&2&7&1&6\\
-6&0&6&1&7&2&8&3&9&4&10&5\\
-7&0&7&3&10&6&2&9&5&1&8&4\\
-8&0&8&5&2&10&7&4&1&9&6&3\\
-9&0&9&7&5&3&1&10&8&6&4&2\\
-10&0&10&9&8&7&6&5&4&3&2&1\\
-\hline
-\end{tabular}
-\end{center}
-\end{figure}
\ No newline at end of file
+	
+	\begin{tikzpicture}[>=latex,thick,scale=0.45]
+		\fill[color=gray!40] (0,0) rectangle (18,-1.5);
+		\fill[color=gray!40] (0,0) rectangle (1.5,-18);	
+		\draw[step = 1.5, gray,very thin] (0,0) grid (18,-18);
+		\draw[very thick] (0,0) rectangle (18,-18);
+		\draw[very thick] (0,-1.5) -- (18,-1.5);
+		\draw[very thick] (1.5,0) -- (1.5,-18);
+		\node at (0.75,-0.75) {$\cdot$};
+		\foreach \x in {0,...,10}
+		\node at (2.25+\x*1.5,-0.75) {$\x$};
+		\foreach \y in {0,...,10}
+		\node at (0.75,-2.25+\y*-1.5) {$\y$};
+		% Row 0
+		\node at ( 2.25,-2.25) {$0$};
+		\node at ( 3.75,-2.25) {$0$};
+		\node at ( 5.25,-2.25) {$0$};
+		\node at ( 6.75,-2.25) {$0$};
+		\node at ( 8.25,-2.25) {$0$};
+		\node at ( 9.75,-2.25) {$0$};
+		\node at (11.25,-2.25) {$0$};
+		\node at (12.75,-2.25) {$0$};
+		\node at (14.25,-2.25) {$0$};
+		\node at (15.75,-2.25) {$0$};
+		\node at (17.25,-2.25) {$0$};
+		% Row 1
+		\node at ( 2.25,-3.75) {$0$};
+		\node at ( 3.75,-3.75) {$1$};
+		\node at ( 5.25,-3.75) {$2$};
+		\node at ( 6.75,-3.75) {$3$};
+		\node at ( 8.25,-3.75) {$4$};
+		\node at ( 9.75,-3.75) {$5$};
+		\node at (11.25,-3.75) {$6$};
+		\node at (12.75,-3.75) {$7$};
+		\node at (14.25,-3.75) {$8$};
+		\node at (15.75,-3.75) {$9$};
+		\node at (17.25,-3.75) {$10$};
+		% Row 2
+		\node at ( 2.25,-5.25) {$0$};
+		\node at ( 3.75,-5.25) {$2$};
+		\node at ( 5.25,-5.25) {$4$};
+		\node at ( 6.75,-5.25) {$6$};
+		\node at ( 8.25,-5.25) {$8$};
+		\node at ( 9.75,-5.25) {$10$};
+		\node at (11.25,-5.25) {$1$};
+		\node at (12.75,-5.25) {$3$};
+		\node at (14.25,-5.25) {$5$};
+		\node at (15.75,-5.25) {$7$};
+		\node at (17.25,-5.25) {$9$};
+		% Row 3
+		\node at ( 2.25,-6.75) {$0$};
+		\node at ( 3.75,-6.75) {$3$};
+		\node at ( 5.25,-6.75) {$6$};
+		\node at ( 6.75,-6.75) {$9$};
+		\node at ( 8.25,-6.75) {$1$};
+		\node at ( 9.75,-6.75) {$4$};
+		\node at (11.25,-6.75) {$7$};
+		\node at (12.75,-6.75) {$10$};
+		\node at (14.25,-6.75) {$2$};
+		\node at (15.75,-6.75) {$5$};
+		\node at (17.25,-6.75) {$8$};
+		% Row 4
+		\node at ( 2.25,-8.25) {$0$};
+		\node at ( 3.75,-8.25) {$4$};
+		\node at ( 5.25,-8.25) {$8$};
+		\node at ( 6.75,-8.25) {$1$};
+		\node at ( 8.25,-8.25) {$5$};
+		\node at ( 9.75,-8.25) {$9$};
+		\node at (11.25,-8.25) {$2$};
+		\node at (12.75,-8.25) {$6$};
+		\node at (14.25,-8.25) {$10$};
+		\node at (15.75,-8.25) {$3$};
+		\node at (17.25,-8.25) {$7$};
+		% Row 5
+		\node at ( 2.25,-9.75) {$0$};
+		\node at ( 3.75,-9.75) {$5$};
+		\node at ( 5.25,-9.75) {$10$};
+		\node at ( 6.75,-9.75) {$4$};
+		\node at ( 8.25,-9.75) {$9$};
+		\node at ( 9.75,-9.75) {$3$};
+		\node at (11.25,-9.75) {$8$};
+		\node at (12.75,-9.75) {$2$};
+		\node at (14.25,-9.75) {$7$};
+		\node at (15.75,-9.75) {$1$};
+		\node at (17.25,-9.75) {$6$};
+		% Row 6
+		\node at ( 2.25,-11.25) {$0$};
+		\node at ( 3.75,-11.25) {$6$};
+		\node at ( 5.25,-11.25) {$1$};
+		\node at ( 6.75,-11.25) {$7$};
+		\node at ( 8.25,-11.25) {$2$};
+		\node at ( 9.75,-11.25) {$8$};
+		\node at (11.25,-11.25) {$3$};
+		\node at (12.75,-11.25) {$9$};
+		\node at (14.25,-11.25) {$4$};
+		\node at (15.75,-11.25) {$10$};
+		\node at (17.25,-11.25) {$5$};
+		% Row 7
+		\node at ( 2.25,-12.75) {$0$};
+		\node at ( 3.75,-12.75) {$7$};
+		\node at ( 5.25,-12.75) {$3$};
+		\node at ( 6.75,-12.75) {$10$};
+		\node at ( 8.25,-12.75) {$6$};
+		\node at ( 9.75,-12.75) {$2$};
+		\node at (11.25,-12.75) {$9$};
+		\node at (12.75,-12.75) {$5$};
+		\node at (14.25,-12.75) {$1$};
+		\node at (15.75,-12.75) {$8$};
+		\node at (17.25,-12.75) {$4$};
+		% Row 8
+		\node at ( 2.25,-14.25) {$0$};
+		\node at ( 3.75,-14.25) {$8$};
+		\node at ( 5.25,-14.25) {$5$};
+		\node at ( 6.75,-14.25) {$2$};
+		\node at ( 8.25,-14.25) {$10$};
+		\node at ( 9.75,-14.25) {$7$};
+		\node at (11.25,-14.25) {$4$};
+		\node at (12.75,-14.25) {$1$};
+		\node at (14.25,-14.25) {$9$};
+		\node at (15.75,-14.25) {$6$};
+		\node at (17.25,-14.25) {$3$};
+		% Row 9
+		\node at ( 2.25,-15.75) {$0$};
+		\node at ( 3.75,-15.75) {$9$};
+		\node at ( 5.25,-15.75) {$7$};
+		\node at ( 6.75,-15.75) {$5$};
+		\node at ( 8.25,-15.75) {$3$};
+		\node at ( 9.75,-15.75) {$1$};
+		\node at (11.25,-15.75) {$10$};
+		\node at (12.75,-15.75) {$8$};
+		\node at (14.25,-15.75) {$6$};
+		\node at (15.75,-15.75) {$4$};
+		\node at (17.25,-15.75) {$2$};
+		% Row 10
+		\node at ( 2.25,-17.25) {$0$};
+		\node at ( 3.75,-17.25) {$10$};
+		\node at ( 5.25,-17.25) {$9$};
+		\node at ( 6.75,-17.25) {$8$};
+		\node at ( 8.25,-17.25) {$7$};
+		\node at ( 9.75,-17.25) {$6$};
+		\node at (11.25,-17.25) {$5$};
+		\node at (12.75,-17.25) {$4$};
+		\node at (14.25,-17.25) {$3$};
+		\node at (15.75,-17.25) {$2$};
+		\node at (17.25,-17.25) {$1$};
+	\end{tikzpicture}
+	
+\end{center}
\ No newline at end of file