aboutsummaryrefslogtreecommitdiffstats
path: root/buch
diff options
context:
space:
mode:
authorJODBaer <JODBaer@github.com>2021-04-21 17:30:50 +0200
committerJODBaer <JODBaer@github.com>2021-04-21 17:30:50 +0200
commit10f3cdb829c001c341ea31415efb44ff6a2878b8 (patch)
tree41705ce3d393160973d719b3f1f4bce3b31abf76 /buch
parentMerge remote-tracking branch 'origin/Baer' into Baer (diff)
downloadSeminarMatrizen-10f3cdb829c001c341ea31415efb44ff6a2878b8.tar.gz
SeminarMatrizen-10f3cdb829c001c341ea31415efb44ff6a2878b8.zip
Persentation stand 17:30
Diffstat (limited to 'buch')
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.aux37
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.log145
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.nav26
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.out4
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.pdfbin117082 -> 132691 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.snm1
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.synctex.gzbin6763 -> 19501 bytes
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.tex109
-rw-r--r--buch/papers/reedsolomon/RS presentation/RS.toc4
9 files changed, 235 insertions, 91 deletions
diff --git a/buch/papers/reedsolomon/RS presentation/RS.aux b/buch/papers/reedsolomon/RS presentation/RS.aux
index fff632d..6294c05 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.aux
+++ b/buch/papers/reedsolomon/RS presentation/RS.aux
@@ -22,10 +22,10 @@
\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}}
\HyPL@Entry{1<</P(2)>>}
-\@writefile{toc}{\beamer@sectionintoc {1}{Introduction}{2}{0}{1}}
+\@writefile{toc}{\beamer@sectionintoc {1}{Einführung}{2}{0}{1}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{1}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{1}}}
-\@writefile{nav}{\headcommand {\sectionentry {1}{Introduction}{2}{Introduction}{0}}}
+\@writefile{nav}{\headcommand {\sectionentry {1}{Einführung}{2}{Einführung}{0}}}
\@writefile{nav}{\headcommand {\slideentry {1}{0}{1}{2/2}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {2}{2}}}
\HyPL@Entry{2<</P(3)>>}
@@ -34,8 +34,33 @@
\HyPL@Entry{9<</P(4)>>}
\@writefile{nav}{\headcommand {\slideentry {1}{0}{3}{10/11}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {10}{11}}}
-\@writefile{nav}{\headcommand {\beamer@partpages {1}{11}}}
-\@writefile{nav}{\headcommand {\beamer@subsectionpages {2}{11}}}
+\HyPL@Entry{11<</P(5)>>}
+\@writefile{toc}{\beamer@sectionintoc {2}{Polynom Ansatz}{12}{0}{2}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {2}{11}}}
-\@writefile{nav}{\headcommand {\beamer@documentpages {11}}}
-\@writefile{nav}{\headcommand {\gdef \inserttotalframenumber {4}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {2}{11}}}
+\@writefile{nav}{\headcommand {\sectionentry {2}{Polynom Ansatz}{12}{Polynom Ansatz}{0}}}
+\@writefile{snm}{\beamer@slide {ft_discrete}{12}}
+\newlabel{ft_discrete}{{5}{12}{Polynom Ansatz}{Doc-Start}{}}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{1}{12/12}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {12}{12}}}
+\HyPL@Entry{12<</P(6)>>}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{2}{13/13}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {13}{13}}}
+\HyPL@Entry{13<</P(7)>>}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{3}{14/15}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {14}{15}}}
+\HyPL@Entry{15<</P(8)>>}
+\@writefile{nav}{\headcommand {\slideentry {2}{0}{4}{16/16}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {16}{16}}}
+\HyPL@Entry{16<</P(9)>>}
+\@writefile{toc}{\beamer@sectionintoc {3}{Diskrete Fourien Transformation}{17}{0}{3}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {12}{16}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {12}{16}}}
+\@writefile{nav}{\headcommand {\sectionentry {3}{Diskrete Fourien Transformation}{17}{Diskrete Fourien Transformation}{0}}}
+\@writefile{nav}{\headcommand {\slideentry {3}{0}{1}{17/17}{}{0}}}
+\@writefile{nav}{\headcommand {\beamer@framepages {17}{17}}}
+\@writefile{nav}{\headcommand {\beamer@partpages {1}{17}}}
+\@writefile{nav}{\headcommand {\beamer@subsectionpages {17}{17}}}
+\@writefile{nav}{\headcommand {\beamer@sectionpages {17}{17}}}
+\@writefile{nav}{\headcommand {\beamer@documentpages {17}}}
+\@writefile{nav}{\headcommand {\gdef \inserttotalframenumber {9}}}
diff --git a/buch/papers/reedsolomon/RS presentation/RS.log b/buch/papers/reedsolomon/RS presentation/RS.log
index 824b9b5..342b031 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.log
+++ b/buch/papers/reedsolomon/RS presentation/RS.log
@@ -1,4 +1,4 @@
-This is XeTeX, Version 3.14159265-2.6-0.999991 (TeX Live 2019/W32TeX) (preloaded format=xelatex 2019.10.25) 21 APR 2021 12:30
+This is XeTeX, Version 3.14159265-2.6-0.999991 (TeX Live 2019/W32TeX) (preloaded format=xelatex 2019.10.25) 21 APR 2021 17:27
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
@@ -972,13 +972,61 @@ Package hyperref Warning: Option `pdfsubject' has already been used,
[1
-] [2
+]
+LaTeX Font Info: Trying to load font information for OT1+lmss on input line
+31.
+ (c:/texlive/2019/texmf-dist/tex/latex/lm/ot1lmss.fd
+File: ot1lmss.fd 2009/10/30 v1.6 Font defs for Latin Modern
+)
+LaTeX Font Info: Trying to load font information for OML+lmm on input line 3
+1.
+
+(c:/texlive/2019/texmf-dist/tex/latex/lm/omllmm.fd
+File: omllmm.fd 2009/10/30 v1.6 Font defs for Latin Modern
+)
+LaTeX Font Info: Trying to load font information for OMS+lmsy on input line
+31.
+
+(c:/texlive/2019/texmf-dist/tex/latex/lm/omslmsy.fd
+File: omslmsy.fd 2009/10/30 v1.6 Font defs for Latin Modern
+)
+LaTeX Font Info: Trying to load font information for OMX+lmex on input line
+31.
+
+(c:/texlive/2019/texmf-dist/tex/latex/lm/omxlmex.fd
+File: omxlmex.fd 2009/10/30 v1.6 Font defs for Latin Modern
+)
+LaTeX Font Info: External font `lmex10' loaded for size
+(Font) <10.95> on input line 31.
+LaTeX Font Info: External font `lmex10' loaded for size
+(Font) <8> on input line 31.
+LaTeX Font Info: External font `lmex10' loaded for size
+(Font) <6> on input line 31.
+LaTeX Font Info: Trying to load font information for U+msa on input line 31.
+
+
+(c:/texlive/2019/texmf-dist/tex/latex/amsfonts/umsa.fd
+File: umsa.fd 2013/01/14 v3.01 AMS symbols A
+)
+LaTeX Font Info: Trying to load font information for U+msb on input line 31.
+
+
+(c:/texlive/2019/texmf-dist/tex/latex/amsfonts/umsb.fd
+File: umsb.fd 2013/01/14 v3.01 AMS symbols B
+)
+LaTeX Font Info: Font shape `T1/lmss/m/it' in size <10.95> not available
+(Font) Font shape `T1/lmss/m/sl' tried instead on input line 31.
+LaTeX Font Info: Font shape `T1/lmss/m/it' in size <8> not available
+(Font) Font shape `T1/lmss/m/sl' tried instead on input line 31.
+LaTeX Font Info: Font shape `T1/lmss/m/it' in size <6> not available
+(Font) Font shape `T1/lmss/m/sl' tried instead on input line 31.
+ [2
]
File: images/fig1.pdf Graphic file (type pdf)
<use images/fig1.pdf>
-Overfull \vbox (14.63716pt too high) detected at line 52
+Overfull \vbox (14.63716pt too high) detected at line 57
[]
[3
@@ -987,7 +1035,7 @@ Overfull \vbox (14.63716pt too high) detected at line 52
File: images/fig2.pdf Graphic file (type pdf)
<use images/fig2.pdf>
-Overfull \vbox (14.63716pt too high) detected at line 52
+Overfull \vbox (14.63716pt too high) detected at line 57
[]
[4
@@ -996,7 +1044,7 @@ Overfull \vbox (14.63716pt too high) detected at line 52
File: images/fig3.pdf Graphic file (type pdf)
<use images/fig3.pdf>
-Overfull \vbox (14.63716pt too high) detected at line 52
+Overfull \vbox (14.63716pt too high) detected at line 57
[]
[5
@@ -1005,7 +1053,7 @@ Overfull \vbox (14.63716pt too high) detected at line 52
File: images/fig4.pdf Graphic file (type pdf)
<use images/fig4.pdf>
-Overfull \vbox (14.63716pt too high) detected at line 52
+Overfull \vbox (14.63716pt too high) detected at line 57
[]
[6
@@ -1014,7 +1062,7 @@ Overfull \vbox (14.63716pt too high) detected at line 52
File: images/fig5.pdf Graphic file (type pdf)
<use images/fig5.pdf>
-Overfull \vbox (14.63716pt too high) detected at line 52
+Overfull \vbox (14.63716pt too high) detected at line 57
[]
[7
@@ -1023,7 +1071,7 @@ Overfull \vbox (14.63716pt too high) detected at line 52
File: images/fig6.pdf Graphic file (type pdf)
<use images/fig6.pdf>
-Overfull \vbox (14.63716pt too high) detected at line 52
+Overfull \vbox (14.63716pt too high) detected at line 57
[]
[8
@@ -1032,67 +1080,32 @@ Overfull \vbox (14.63716pt too high) detected at line 52
File: images/fig7.pdf Graphic file (type pdf)
<use images/fig7.pdf>
-Overfull \vbox (14.63716pt too high) detected at line 52
+Overfull \vbox (14.63716pt too high) detected at line 57
[]
[9
-]
-LaTeX Font Info: Trying to load font information for OT1+lmss on input line
-66.
- (c:/texlive/2019/texmf-dist/tex/latex/lm/ot1lmss.fd
-File: ot1lmss.fd 2009/10/30 v1.6 Font defs for Latin Modern
-)
-LaTeX Font Info: Trying to load font information for OML+lmm on input line 6
-6.
-
-(c:/texlive/2019/texmf-dist/tex/latex/lm/omllmm.fd
-File: omllmm.fd 2009/10/30 v1.6 Font defs for Latin Modern
-)
-LaTeX Font Info: Trying to load font information for OMS+lmsy on input line
-66.
-
-(c:/texlive/2019/texmf-dist/tex/latex/lm/omslmsy.fd
-File: omslmsy.fd 2009/10/30 v1.6 Font defs for Latin Modern
-)
-LaTeX Font Info: Trying to load font information for OMX+lmex on input line
-66.
-
-(c:/texlive/2019/texmf-dist/tex/latex/lm/omxlmex.fd
-File: omxlmex.fd 2009/10/30 v1.6 Font defs for Latin Modern
-)
-LaTeX Font Info: External font `lmex10' loaded for size
-(Font) <10.95> on input line 66.
-LaTeX Font Info: External font `lmex10' loaded for size
-(Font) <8> on input line 66.
-LaTeX Font Info: External font `lmex10' loaded for size
-(Font) <6> on input line 66.
-LaTeX Font Info: Trying to load font information for U+msa on input line 66.
+] [10
+] [11
-(c:/texlive/2019/texmf-dist/tex/latex/amsfonts/umsa.fd
-File: umsa.fd 2013/01/14 v3.01 AMS symbols A
-)
-LaTeX Font Info: Trying to load font information for U+msb on input line 66.
+] [12
+] [13
-(c:/texlive/2019/texmf-dist/tex/latex/amsfonts/umsb.fd
-File: umsb.fd 2013/01/14 v3.01 AMS symbols B
-)
-LaTeX Font Info: Font shape `T1/lmss/m/it' in size <10.95> not available
-(Font) Font shape `T1/lmss/m/sl' tried instead on input line 66.
-LaTeX Font Info: Font shape `T1/lmss/m/it' in size <8> not available
-(Font) Font shape `T1/lmss/m/sl' tried instead on input line 66.
-LaTeX Font Info: Font shape `T1/lmss/m/it' in size <6> not available
-(Font) Font shape `T1/lmss/m/sl' tried instead on input line 66.
+]
File: images/polynom1.pdf Graphic file (type pdf)
<use images/polynom1.pdf>
- [10
+ [14
]
File: images/polynom2.pdf Graphic file (type pdf)
<use images/polynom2.pdf>
- [11
+ [15
+
+] [16
+
+] [17
]
\tf@nav=\write6
@@ -1104,21 +1117,21 @@ File: images/polynom2.pdf Graphic file (type pdf)
\tf@snm=\write8
\openout8 = `RS.snm'.
-Package atveryend Info: Empty hook `BeforeClearDocument' on input line 68.
-Package atveryend Info: Empty hook `AfterLastShipout' on input line 68.
+Package atveryend Info: Empty hook `BeforeClearDocument' on input line 154.
+Package atveryend Info: Empty hook `AfterLastShipout' on input line 154.
(./RS.aux)
-Package atveryend Info: Empty hook `AtVeryEndDocument' on input line 68.
-Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 68.
+Package atveryend Info: Empty hook `AtVeryEndDocument' on input line 154.
+Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 154.
Package rerunfilecheck Info: File `RS.out' has not changed.
-(rerunfilecheck) Checksum: 4CA0FF56E3EE124326A4720E136735D1.
+(rerunfilecheck) Checksum: 488F938CBAD5E8FAC29F906360775E5F.
)
Here is how much of TeX's memory you used:
- 24329 strings out of 492483
- 450480 string characters out of 6132858
- 528380 words of memory out of 5000000
- 28307 multiletter control sequences out of 15000+600000
+ 24397 strings out of 492483
+ 452001 string characters out of 6132858
+ 533692 words of memory out of 5000000
+ 28375 multiletter control sequences out of 15000+600000
37892 words of font info for 41 fonts, out of 8000000 for 9000
1348 hyphenation exceptions out of 8191
- 58i,15n,57p,796b,539s stack positions out of 5000i,500n,10000p,200000b,80000s
+ 58i,15n,61p,796b,549s stack positions out of 5000i,500n,10000p,200000b,80000s
-Output written on RS.pdf (11 pages).
+Output written on RS.pdf (17 pages).
diff --git a/buch/papers/reedsolomon/RS presentation/RS.nav b/buch/papers/reedsolomon/RS presentation/RS.nav
index 3edba3c..22ae94a 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.nav
+++ b/buch/papers/reedsolomon/RS presentation/RS.nav
@@ -2,15 +2,31 @@
\headcommand {\beamer@framepages {1}{1}}
\headcommand {\beamer@sectionpages {1}{1}}
\headcommand {\beamer@subsectionpages {1}{1}}
-\headcommand {\sectionentry {1}{Introduction}{2}{Introduction}{0}}
+\headcommand {\sectionentry {1}{Einführung}{2}{Einführung}{0}}
\headcommand {\slideentry {1}{0}{1}{2/2}{}{0}}
\headcommand {\beamer@framepages {2}{2}}
\headcommand {\slideentry {1}{0}{2}{3/9}{}{0}}
\headcommand {\beamer@framepages {3}{9}}
\headcommand {\slideentry {1}{0}{3}{10/11}{}{0}}
\headcommand {\beamer@framepages {10}{11}}
-\headcommand {\beamer@partpages {1}{11}}
-\headcommand {\beamer@subsectionpages {2}{11}}
\headcommand {\beamer@sectionpages {2}{11}}
-\headcommand {\beamer@documentpages {11}}
-\headcommand {\gdef \inserttotalframenumber {4}}
+\headcommand {\beamer@subsectionpages {2}{11}}
+\headcommand {\sectionentry {2}{Polynom Ansatz}{12}{Polynom Ansatz}{0}}
+\headcommand {\slideentry {2}{0}{1}{12/12}{}{0}}
+\headcommand {\beamer@framepages {12}{12}}
+\headcommand {\slideentry {2}{0}{2}{13/13}{}{0}}
+\headcommand {\beamer@framepages {13}{13}}
+\headcommand {\slideentry {2}{0}{3}{14/15}{}{0}}
+\headcommand {\beamer@framepages {14}{15}}
+\headcommand {\slideentry {2}{0}{4}{16/16}{}{0}}
+\headcommand {\beamer@framepages {16}{16}}
+\headcommand {\beamer@sectionpages {12}{16}}
+\headcommand {\beamer@subsectionpages {12}{16}}
+\headcommand {\sectionentry {3}{Diskrete Fourien Transformation}{17}{Diskrete Fourien Transformation}{0}}
+\headcommand {\slideentry {3}{0}{1}{17/17}{}{0}}
+\headcommand {\beamer@framepages {17}{17}}
+\headcommand {\beamer@partpages {1}{17}}
+\headcommand {\beamer@subsectionpages {17}{17}}
+\headcommand {\beamer@sectionpages {17}{17}}
+\headcommand {\beamer@documentpages {17}}
+\headcommand {\gdef \inserttotalframenumber {9}}
diff --git a/buch/papers/reedsolomon/RS presentation/RS.out b/buch/papers/reedsolomon/RS presentation/RS.out
index dec2d7d..597a5f8 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.out
+++ b/buch/papers/reedsolomon/RS presentation/RS.out
@@ -1 +1,3 @@
-\BOOKMARK [2][]{Outline0.1}{Introduction}{}% 1
+\BOOKMARK [2][]{Outline0.1}{Einführung}{}% 1
+\BOOKMARK [2][]{Outline0.2}{Polynom\040Ansatz}{}% 2
+\BOOKMARK [2][]{Outline0.3}{Diskrete\040Fourien\040Transformation}{}% 3
diff --git a/buch/papers/reedsolomon/RS presentation/RS.pdf b/buch/papers/reedsolomon/RS presentation/RS.pdf
index 10719b7..f49671f 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.pdf
+++ b/buch/papers/reedsolomon/RS presentation/RS.pdf
Binary files differ
diff --git a/buch/papers/reedsolomon/RS presentation/RS.snm b/buch/papers/reedsolomon/RS presentation/RS.snm
index e69de29..8b82641 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.snm
+++ b/buch/papers/reedsolomon/RS presentation/RS.snm
@@ -0,0 +1 @@
+\beamer@slide {ft_discrete}{12}
diff --git a/buch/papers/reedsolomon/RS presentation/RS.synctex.gz b/buch/papers/reedsolomon/RS presentation/RS.synctex.gz
index 2fe95de..96af4cc 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.synctex.gz
+++ b/buch/papers/reedsolomon/RS presentation/RS.synctex.gz
Binary files differ
diff --git a/buch/papers/reedsolomon/RS presentation/RS.tex b/buch/papers/reedsolomon/RS presentation/RS.tex
index fb822da..9bdf947 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.tex
+++ b/buch/papers/reedsolomon/RS presentation/RS.tex
@@ -19,10 +19,15 @@
\begin{frame}[plain]
\maketitle
\end{frame}
- \section{Introduction}
+ \section{Einführung}
\begin{frame}
\frametitle{Idee}
-
+ \begin{itemize}
+ \item Reed-Solomon-Code beschäftigt sich mit der Übertragung von Daten
+ und deren Fehler Erkennung.
+ \item Idee Fourier Transformieren und dann senden.
+ \item Danach Empfangen und Rücktransformieren.
+ \end{itemize}
\end{frame}
\begin{frame}
@@ -50,20 +55,100 @@
}
\end{figure}
\end{frame}
+
\begin{frame}
- Übertragen von den Zahlen
- \textcolor{blue}{2}, \textcolor{blue}{1}, \textcolor{blue}{5}
- als $ p(x) = \textcolor{blue}{2}x^2 + \textcolor{blue}{1}x + \textcolor{blue}{5} $.\newline
- Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8},
- \textcolor{green}{15}, \textcolor{green}{26},
- \textcolor{green}{ 41}, \textcolor{green}{60},
- \textcolor{green}{83}, \textcolor{green}{110})$
+ \uncover<1->{
+ Wie ist die Anzahl 0 definiert zum mitgeben?
+ Indem die Polymereigenschaft genutzt werden.
+ }
+ \uncover<2->{
+ Wie wird der Fehler lokalisiert?
+ Indem in einem Endlichen Körper gerechnet wird.
+ }
+
+ \end{frame}
+
+\section{Polynom Ansatz}
+ \begin{frame}
+ Die Diskrite Fouren Transformation ist so gegeben
+ \[
+ \label{ft_discrete}
+ \hat{c}_{k}
+ = \frac{1}{N} \sum_{n=0}^{N-1}
+ {f}_n \cdot e^{-\frac{2\pi j}{N} \cdot kn}
+ \].
+
+ \[
+ w = e^{-\frac{2\pi j}{N} k}
+ \]
+ Wenn $N$ konstant:
+ \[
+ \hat{c}_{k}=\frac{1}{N}( {f}_0 w^0 + {f}_1 w^1 + {f}_2 w^2 + \dots + {f}_{N-1} w^N)
+ \]
+ \end{frame}
+
+ \begin{frame}
+ Beispiel 2, 1, 5 Versenden und auf 2 Fehler absichern.
+ \end{frame}
+ \begin{frame}
+ Übertragen von
+ ${f}_2=$\textcolor{blue}{2}, ${f}_1$\textcolor{blue}{1}, ${f}_0$\textcolor{blue}{5}
+ als $ p(w) = \textcolor{blue}{2}w^2 + \textcolor{blue}{1}w + \textcolor{blue}{5} $.
+
\only<1>{
- \includegraphics[]{images/polynom1.pdf}}
+ Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8},
+ \textcolor{green}{15}, \textcolor{green}{26},
+ \textcolor{green}{ 41}, \textcolor{green}{60},
+ \textcolor{green}{83}, \textcolor{green}{110})$
+ \includegraphics[scale = 1.2]{images/polynom1.pdf}}
\only<2>{
- \includegraphics[]{images/polynom2.pdf}}
+ Versende $ (p(1),p(2),...,p(7)) = (\textcolor{green}{8},
+ \textcolor{red}{50}, \textcolor{red}{37},
+ \textcolor{green}{ 41}, \textcolor{green}{60},
+ \textcolor{green}{83}, \textcolor{green}{110})$
+ \includegraphics[scale = 1.2]{images/polynom2.pdf}
+ \textcolor{green}{7} Zahlen versenden, um \textcolor{blue}{3} Zahlen gegen \textcolor{red}{2} Fehlern abzusichern.}
+ \end{frame}
+
+ \begin{frame}
+ \frametitle{Parameter}
+ \begin{center}
+ \begin{tabular}{ c c c }
+ \hline
+ "Nutzlast" & Fehler & Versenden \\
+ \hline
+ 3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\
+ 4 & 2 & 8 Werte eines Polynoms vom Grad 3 \\
+ 3 & 2 & 7 Werte eines Polynoms vom Grad 2 \\
+ &&\\
+ k & t & k+2t Werte eines Polynoms vom Grad k-1 \\
+ \hline
+ \end{tabular}
+ \end{center}
+ \end{frame}
+\section{Diskrete Fourien Transformation}
+ \begin{frame}
+ \[
+ \begin{pmatrix}
+ \hat{c}_1 \\\hat{c}_2 \\\hat{c}_3 \\ \vdots \\\hat{c}_n
+ \end{pmatrix}
+ =
+ \begin{pmatrix}
+ w^0 & w^0 & w^0 & \dots &w^0 \\
+ w^0 & w^1 &w^2 & \dots &w^n \\
+ w^0 & w^2 &w^4 & \dots &w^{2n} \\
+ \vdots & \vdots &\vdots &\ddots &\vdots \\
+ w^0 & w^{1n}&w^{2n}& \dots &w^{n} \\
+ \end{pmatrix}
+ \begin{pmatrix}
+ \textcolor{blue}{5} \\
+ \textcolor{blue}{1} \\
+ \textcolor{blue}{2} \\
+ \vdots \\
+ 0 \\
+ \end{pmatrix}
+ \]
\end{frame}
-
\end{document} \ No newline at end of file
diff --git a/buch/papers/reedsolomon/RS presentation/RS.toc b/buch/papers/reedsolomon/RS presentation/RS.toc
index 32e7e8d..ff200c6 100644
--- a/buch/papers/reedsolomon/RS presentation/RS.toc
+++ b/buch/papers/reedsolomon/RS presentation/RS.toc
@@ -1,2 +1,4 @@
\babel@toc {ngerman}{}
-\beamer@sectionintoc {1}{Introduction}{2}{0}{1}
+\beamer@sectionintoc {1}{Einführung}{2}{0}{1}
+\beamer@sectionintoc {2}{Polynom Ansatz}{12}{0}{2}
+\beamer@sectionintoc {3}{Diskrete Fourien Transformation}{17}{0}{3}